env stringclasses 1 value | prompt stringlengths 119 673 | extra dict |
|---|---|---|
logic-v2 | Define ○, the rules are as follows:
when x is odd, x ○ y = x ** y + x - x;
otherwise, x ○ y = y * x / x - x + x.
The precedence of operations: ** = ○ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 6
Please fill your final answer in \boxed{}. | {
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logic-v2 | 定义 ⊗，规则如下：
实数域上，x ⊗ y = x + x - y。
和 ▽，规则如下：
当x和y都是奇数时，x ▽ y = y - x + y；
其他情况下，x ▽ y = y + y * x。
和 △，规则如下：
实数域上，x △ y = y ▽ x * x。
运算优先级：⊗ > ** = ▽ = △ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5 ▽ 9 ⊗ 2 △ 4
请将最终答案填入\boxed{}中。 | {
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"question": "定义 ⊗，规则如下：\n实数域上，x ⊗ y = x + x - y。\n和 ▽，规则如下：\n当x和y都是奇数时，x ▽ y = y - x + y；\n其他情况下，x ▽ y = y + y * x。\n和 △，规则如下：\n实数域上，x △ y = y ▽ x * x。\n运算优先级：⊗ > ** = ▽ = △ > * = / = % > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 5 ▽ 9 ⊗ 2 △ 4\n请将最终答案填入\\boxed{}中。"
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"default_operation": " y ▽ x * x",
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"▽": {
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"conditions": [
{
"condition": "x和y都是奇数",
"operation": " y - x + y"
}
],
"default_operation": " y + y * x",
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logic-v2 | Define ○, the rules are as follows:
when x is odd, x ○ y = y / x - 4;
otherwise, x ○ y = (x - y - x).
The precedence of operations: ** > * = / = % > + = - = ○。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 6 ** 5 ○ 6 - 1
Please fill your final answer in \boxed{}. | {
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},
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logic-v2 | Define ⊙, the rules are as follows:
when x is odd, x ⊙ y = x + x + y;
otherwise, x ⊙ y = x + y - x.
and ◎, the rules are as follows:
when x is a multiple of 3, x ◎ y = y * x + x;
otherwise, x ◎ y = y + x + x.
and ⊕, the rules are as follows:
on the real number field, x ⊕ y = x + (3 + y).
The precedence of operations: ⊙ = ◎ = ⊕ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 1 ◎ 4 ⊙ 3 ⊕ 7
Please fill your final answer in \boxed{}. | {
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logic-v2 | 定义 ⊙，规则如下：
实数域上，x ⊙ y = y * x - x。
和 ◎，规则如下：
当x等于y时，x ◎ y = y - (y) * x；
其他情况下，x ◎ y = y - x / y / y。
和 ⊕，规则如下：
当y是奇数时，x ⊕ y = 1 / (x + y) ⊙ y；
其他情况下，x ⊕ y = y * 5 * 1 - x。
运算优先级：⊙ = ◎ > ** = ⊕ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 / 3 ◎ 7 ⊕ 5 / 3 ⊙ 6
请将最终答案填入\boxed{}中。 | {
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logic-v2 | 定义 ▽，规则如下：
实数域上，x ▽ y = y / x - x。
运算优先级：** > * = / = % > + = - = ▽。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5
请将最终答案填入\boxed{}中。 | {
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logic-v2 | 定义 ♢，规则如下：
当x大于y时，x ♢ y = x + y；
其他情况下，x ♢ y = (5 * y - x + x)。
和 ☆，规则如下：
当x和y都是奇数时，x ☆ y = y - y ♢ 4 / x；
其他情况下，x ☆ y = y - x ♢ x * y。
和 ⊗，规则如下：
实数域上，x ⊗ y = 2 / x - 4 / y。
运算优先级：** = ♢ = ⊗ > * = / = % = ☆ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 ⊗ 9 ☆ 3 ♢ 2
请将最终答案填入\boxed{}中。 | {
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},
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"solutions_count": null,
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logic-v2 | Define ○, the rules are as follows:
when x and y are both odd, x ○ y = abs(y * x);
otherwise, x ○ y = abs(x - x - y).
The precedence of operations: ** > * = / = % = ○ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 9 ○ 6
Please fill your final answer in \boxed{}. | {
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},
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"○": {
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logic-v2 | 定义 ☆，规则如下：
当x是偶数时，x ☆ y = y + y + x * x；
其他情况下，x ☆ y = y / y + x。
和 ▽，规则如下：
当y是5的倍数时，x ▽ y = y / y - y - x；
其他情况下，x ▽ y = x * y * x。
运算优先级：▽ > ** > * = / = % = ☆ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 ☆ 2 ▽ 3
请将最终答案填入\boxed{}中。 | {
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"question": "定义 ☆，规则如下：\n当x是偶数时，x ☆ y = y + y + x * x；\n其他情况下，x ☆ y = y / y + x。\n和 ▽，规则如下：\n当y是5的倍数时，x ▽ y = y / y - y - x；\n其他情况下，x ▽ y = x * y * x。\n运算优先级：▽ > ** > * = / = % = ☆ > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 4 ☆ 2 ▽ 3\n请将最终答案填入\\boxed{}中。"
},
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} |
logic-v2 | 定义 □，规则如下：
实数域上，x □ y = x * y - y。
和 ⊙，规则如下：
当x和y的和是偶数时，x ⊙ y = y - y - x；
其他情况下，x ⊙ y = x * y - x。
运算优先级：□ > ** > * = / = % = ⊙ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 / 4 □ 3 + 4 ⊙ 10
请将最终答案填入\boxed{}中。 | {
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"question": "定义 □，规则如下：\n实数域上，x □ y = x * y - y。\n和 ⊙，规则如下：\n当x和y的和是偶数时，x ⊙ y = y - y - x；\n其他情况下，x ⊙ y = x * y - x。\n运算优先级：□ > ** > * = / = % = ⊙ > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 6 / 4 □ 3 + 4 ⊙ 10\n请将最终答案填入\\boxed{}中。"
},
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},
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"seed": 9010043,
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} |
logic-v2 | Define ♡, the rules are as follows:
on the real number field, x ♡ y = y + (x - x + x) - y.
and △, the rules are as follows:
when x is a multiple of 5, x △ y = y + y - y * x ♡ x;
otherwise, x △ y = x / x ** y + 2.
The precedence of operations: ♡ > ** = △ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 3 ♡ 3
Please fill your final answer in \boxed{}. | {
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},
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"◎": null,
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"♡": {
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"conditions": [],
"default_operation": " y + (x - x + x) - y",
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},
"♢": null
},
"target": null,
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},
"seed": 40524476,
"task_id": 240524476,
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} |
logic-v2 | Define ▽, the rules are as follows:
when y is a multiple of 3, x ▽ y = y - abs(x - x * y);
otherwise, x ▽ y = abs(x + y).
The precedence of operations: ** > * = / = % = ▽ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 3 / 5 ▽ 4
Please fill your final answer in \boxed{}. | {
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},
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logic-v2 | Define □, the rules are as follows:
on the real number field, x □ y = y ** x.
and △, the rules are as follows:
when x is greater than y, x △ y = x ** y + x + y;
otherwise, x △ y = x + y + y + y.
The precedence of operations: □ > ** = △ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 10 △ 9 □ 4 □ 1
Please fill your final answer in \boxed{}. | {
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},
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"seed": 60949218,
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} |
logic-v2 | 定义 △，规则如下：
当x是3的倍数时，x △ y = y - y * x；
其他情况下，x △ y = y + y / y * y - x。
运算优先级：△ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 △ 4 △ 3 / 4
请将最终答案填入\boxed{}中。 | {
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},
"seed": 28096018,
"task_id": 228096018,
"task_type": "operation"
} |
logic-v2 | Define ◇, the rules are as follows:
on the real number field, x ◇ y = x * y + y.
The precedence of operations: ◇ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 1
Please fill your final answer in \boxed{}. | {
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},
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"△": null,
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},
"○": null,
"◎": null,
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logic-v2 | 定义 ☆，规则如下：
当x是5的倍数时，x ☆ y = (y) + x；
其他情况下，x ☆ y = (y - x * y - x)。
和 △，规则如下：
当x和y的和是奇数时，x △ y = x - x ** x + x ☆ y；
其他情况下，x △ y = y - y ☆ x - y + x。
运算优先级：** = ☆ > * = / = % > + = - = △。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ☆ 2 △ 4
请将最终答案填入\boxed{}中。 | {
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"answer": "9",
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"expression": "1 ☆ 2 △ 4",
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"default_operation": " y - y ☆ x - y + x",
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"▽": null,
"◇": null,
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],
"default_operation": " (y - x * y - x)",
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},
"♡": null,
"♢": null
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"target": null,
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"question": "定义 ☆，规则如下：\n当x是5的倍数时，x ☆ y = (y) + x；\n其他情况下，x ☆ y = (y - x * y - x)。\n和 △，规则如下：\n当x和y的和是奇数时，x △ y = x - x ** x + x ☆ y；\n其他情况下，x △ y = y - y ☆ x - y + x。\n运算优先级：** = ☆ > * = / = % > + = - = △。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 1 ☆ 2 △ 4\n请将最终答案填入\\boxed{}中。"
},
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"△": {
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],
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},
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"◇": null,
"○": null,
"◎": null,
"☆": {
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"conditions": [
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"operation": " (y) + x"
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],
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"♡": null,
"♢": null
},
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},
"seed": 80071333,
"task_id": 280071333,
"task_type": "operation"
} |
logic-v2 | Define △, the rules are as follows:
when y is odd, x △ y = (y) / 5 - 5 + y + x;
otherwise, x △ y = 4 / y + x - 3 - y.
The precedence of operations: ** > * = / = % = △ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 2
Please fill your final answer in \boxed{}. | {
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},
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"⊙": null,
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"△": {
"associativity": "left",
"conditions": [
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"condition": "y是奇数",
"operation": " (y) / 5 - 5 + y + x"
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],
"default_operation": " 4 / y + x - 3 - y",
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"▽": null,
"◇": null,
"○": null,
"◎": null,
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logic-v2 | Define △, the rules are as follows:
on the real number field, x △ y = x / y - x.
The precedence of operations: △ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 4 △ 3
Please fill your final answer in \boxed{}. | {
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},
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},
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
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"seed": 58211699,
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} |
logic-v2 | Define ♢, the rules are as follows:
on the real number field, x ♢ y = y * y * y * x * x.
and ○, the rules are as follows:
on the real number field, x ○ y = x * x * x / y ** y.
and ♡, the rules are as follows:
on the real number field, x ♡ y = y - 2 ♢ x + x.
The precedence of operations: ♢ = ○ = ♡ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 7 ○ 9 ♡ 1 ♢ 7
Please fill your final answer in \boxed{}. | {
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"□": null,
"△": null,
"▽": null,
"◇": null,
"○": {
"associativity": "left",
"conditions": [],
"default_operation": " x * x * x / y ** y",
"precedence": 5
},
"◎": null,
"☆": null,
"♡": {
"associativity": "left",
"conditions": [],
"default_operation": " y - 2 ♢ x + x",
"precedence": 5
},
"♢": {
"associativity": "left",
"conditions": [],
"default_operation": " y * y * y * x * x",
"precedence": 5
}
},
"target": null,
"total_length": null,
"trace_id": "758abcd7-9b87-48c4-9204-43352acf02e5"
},
"question": "Define ♢, the rules are as follows:\non the real number field, x ♢ y = y * y * y * x * x.\nand ○, the rules are as follows:\non the real number field, x ○ y = x * x * x / y ** y.\nand ♡, the rules are as follows:\non the real number field, x ♡ y = y - 2 ♢ x + x.\nThe precedence of operations: ♢ = ○ = ♡ > ** > * = / = % > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 7 ○ 9 ♡ 1 ♢ 7\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
"closing_sequence": null,
"expression": "7 ○ 9 ♡ 1 ♢ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null,
"num_of_numbers": null,
"num_symbols": 3,
"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 66388282,
"simplified_expr": "( 7 * 7 * 7 * (((((1 - (( ((((((7 * 7)) * 7)) / ((9 ** 9)))) * ((((((7 * 7)) * 7)) / ((9 ** 9)))) * ((((((7 * 7)) * 7)) / ((9 ** 9)))) * 2 * 2)))) + ((((((7 * 7)) * 7)) / ((9 ** 9))))))) * (((((1 - (( ((((((7 * 7)) * 7)) / ((9 ** 9)))) * ((((((7 * 7)) * 7)) / ((9 ** 9)))) * ((((((7 * 7)) * 7)) / ((9 ** 9)))) * 2 * 2)))) + ((((((7 * 7)) * 7)) / ((9 ** 9))))))))",
"solutions_count": null,
"symbol_definitions": {
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"○": {
"associativity": "left",
"conditions": [],
"default_operation": " x * x * x / y ** y",
"precedence": 5
},
"◎": null,
"☆": null,
"♡": {
"associativity": "left",
"conditions": [],
"default_operation": " y - 2 ♢ x + x",
"precedence": 5
},
"♢": {
"associativity": "left",
"conditions": [],
"default_operation": " y * y * y * x * x",
"precedence": 5
}
},
"target": null,
"total_length": null,
"trace_id": "758abcd7-9b87-48c4-9204-43352acf02e5"
},
"seed": 66388282,
"task_id": 266388282,
"task_type": "operation"
} |
logic-v2 | Define ○, the rules are as follows:
when y is a multiple of 5, x ○ y = x ** x + x + x + y;
otherwise, x ○ y = x - x + x * y.
The precedence of operations: ○ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 1 ** 8 ○ 9 / 1
Please fill your final answer in \boxed{}. | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ** 8 ○ 9 / 1",
"fill_length": null,
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"n_types": null,
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"num_of_numbers": null,
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"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 891049,
"simplified_expr": "(((1 ** (( 8 - 8 + 8 * 9)))) / 1)",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": {
"associativity": "left",
"conditions": [
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"condition": "y是5的倍数",
"operation": " x ** x + x + x + y"
}
],
"default_operation": " x - x + x * y",
"precedence": 4
},
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "cdf9d289-be5d-4c52-98b5-2467b67eb906"
},
"question": "Define ○, the rules are as follows:\nwhen y is a multiple of 5, x ○ y = x ** x + x + x + y;\notherwise, x ○ y = x - x + x * y.\nThe precedence of operations: ○ > ** > * = / = % > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 1 ** 8 ○ 9 / 1\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
"closing_sequence": null,
"expression": "1 ** 8 ○ 9 / 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null,
"num_of_numbers": null,
"num_symbols": 1,
"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 891049,
"simplified_expr": "(((1 ** (( 8 - 8 + 8 * 9)))) / 1)",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": {
"associativity": "left",
"conditions": [
{
"condition": "y是5的倍数",
"operation": " x ** x + x + x + y"
}
],
"default_operation": " x - x + x * y",
"precedence": 4
},
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "cdf9d289-be5d-4c52-98b5-2467b67eb906"
},
"seed": 891049,
"task_id": 200891049,
"task_type": "operation"
} |
logic-v2 | Define ◎, the rules are as follows:
on the real number field, x ◎ y = 5 + y + 3 - x * 4.
and △, the rules are as follows:
on the real number field, x △ y = y - y - x ◎ x * y.
The precedence of operations: ◎ > ** > * = / = % > + = - = △。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 6 △ 9 ◎ 9 ◎ 8
Please fill your final answer in \boxed{}. | {
"game_data": {
"answer": "920",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 △ 9 ◎ 9 ◎ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null,
"num_of_numbers": null,
"num_symbols": 2,
"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 50647257,
"simplified_expr": "((((((((((5 + 8)) + 3)) - ((((((((5 + 9)) + 3)) - ((9 * 4)))) * 4)))) - ((((((5 + 8)) + 3)) - ((((((((5 + 9)) + 3)) - ((9 * 4)))) * 4)))))) - (((( 5 + 6 + 3 - 6 * 4)) * ((((((5 + 8)) + 3)) - ((((((((5 + 9)) + 3)) - ((9 * 4)))) * 4))))))))",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": {
"associativity": "left",
"conditions": [],
"default_operation": " y - y - x ◎ x * y",
"precedence": 1
},
"▽": null,
"◇": null,
"○": null,
"◎": {
"associativity": "left",
"conditions": [],
"default_operation": " 5 + y + 3 - x * 4",
"precedence": 4
},
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "fab913f6-ae52-4184-8a86-c932abf951df"
},
"question": "Define ◎, the rules are as follows:\non the real number field, x ◎ y = 5 + y + 3 - x * 4.\nand △, the rules are as follows:\non the real number field, x △ y = y - y - x ◎ x * y.\nThe precedence of operations: ◎ > ** > * = / = % > + = - = △。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 6 △ 9 ◎ 9 ◎ 8\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
"closing_sequence": null,
"expression": "6 △ 9 ◎ 9 ◎ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null,
"num_of_numbers": null,
"num_symbols": 2,
"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 50647257,
"simplified_expr": "((((((((((5 + 8)) + 3)) - ((((((((5 + 9)) + 3)) - ((9 * 4)))) * 4)))) - ((((((5 + 8)) + 3)) - ((((((((5 + 9)) + 3)) - ((9 * 4)))) * 4)))))) - (((( 5 + 6 + 3 - 6 * 4)) * ((((((5 + 8)) + 3)) - ((((((((5 + 9)) + 3)) - ((9 * 4)))) * 4))))))))",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": {
"associativity": "left",
"conditions": [],
"default_operation": " y - y - x ◎ x * y",
"precedence": 1
},
"▽": null,
"◇": null,
"○": null,
"◎": {
"associativity": "left",
"conditions": [],
"default_operation": " 5 + y + 3 - x * 4",
"precedence": 4
},
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "fab913f6-ae52-4184-8a86-c932abf951df"
},
"seed": 50647257,
"task_id": 250647257,
"task_type": "operation"
} |
logic-v2 | Define □, the rules are as follows:
on the real number field, x □ y = x / y * x - y * x.
and ◇, the rules are as follows:
when x is equal to y, x ◇ y = x - y * x □ x;
otherwise, x ◇ y = x * y - 3 * y.
The precedence of operations: ** = ◇ > * = / = % = □ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 2 □ 5
Please fill your final answer in \boxed{}. | {
"game_data": {
"answer": "-9.2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 □ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null,
"num_of_numbers": null,
"num_symbols": 2,
"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 5356496,
"simplified_expr": "( 2 / 5 * 2 - 5 * 2)",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": {
"associativity": "left",
"conditions": [],
"default_operation": " x / y * x - y * x",
"precedence": 2
},
"△": null,
"▽": null,
"◇": {
"associativity": "left",
"conditions": [
{
"condition": "x等于y",
"operation": " x - y * x □ x"
}
],
"default_operation": " x * y - 3 * y",
"precedence": 3
},
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "c0a618d0-5d0b-4458-b3b3-c7fd7d60b0f3"
},
"question": "Define □, the rules are as follows:\non the real number field, x □ y = x / y * x - y * x.\nand ◇, the rules are as follows:\nwhen x is equal to y, x ◇ y = x - y * x □ x;\notherwise, x ◇ y = x * y - 3 * y.\nThe precedence of operations: ** = ◇ > * = / = % = □ > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 2 □ 5\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
"closing_sequence": null,
"expression": "2 □ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null,
"num_of_numbers": null,
"num_symbols": 2,
"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 5356496,
"simplified_expr": "( 2 / 5 * 2 - 5 * 2)",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": {
"associativity": "left",
"conditions": [],
"default_operation": " x / y * x - y * x",
"precedence": 2
},
"△": null,
"▽": null,
"◇": {
"associativity": "left",
"conditions": [
{
"condition": "x等于y",
"operation": " x - y * x □ x"
}
],
"default_operation": " x * y - 3 * y",
"precedence": 3
},
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "c0a618d0-5d0b-4458-b3b3-c7fd7d60b0f3"
},
"seed": 5356496,
"task_id": 205356496,
"task_type": "operation"
} |
logic-v2 | Define ▽, the rules are as follows:
when y is odd, x ▽ y = x + x * y;
otherwise, x ▽ y = x * y * y ** x.
The precedence of operations: ▽ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 2 ▽ 9 % 5
Please fill your final answer in \boxed{}. | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ▽ 9 % 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
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"num_of_numbers": null,
"num_symbols": 1,
"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 94042447,
"simplified_expr": "((( 2 + 2 * 9)) % 5)",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": null,
"▽": {
"associativity": "left",
"conditions": [
{
"condition": "y是奇数",
"operation": " x + x * y"
}
],
"default_operation": " x * y * y ** x",
"precedence": 4
},
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "8eb49dfb-c1b9-43ba-b141-4389af4d0cdb"
},
"question": "Define ▽, the rules are as follows:\nwhen y is odd, x ▽ y = x + x * y;\notherwise, x ▽ y = x * y * y ** x.\nThe precedence of operations: ▽ > ** > * = / = % > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 2 ▽ 9 % 5\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
"closing_sequence": null,
"expression": "2 ▽ 9 % 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null,
"num_of_numbers": null,
"num_symbols": 1,
"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 94042447,
"simplified_expr": "((( 2 + 2 * 9)) % 5)",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": null,
"▽": {
"associativity": "left",
"conditions": [
{
"condition": "y是奇数",
"operation": " x + x * y"
}
],
"default_operation": " x * y * y ** x",
"precedence": 4
},
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "8eb49dfb-c1b9-43ba-b141-4389af4d0cdb"
},
"seed": 94042447,
"task_id": 294042447,
"task_type": "operation"
} |
logic-v2 | Define ◎, the rules are as follows:
when x and y are both even, x ◎ y = y - 4 - x - x;
otherwise, x ◎ y = y - x + y.
and ☆, the rules are as follows:
on the real number field, x ☆ y = y + y * x + x.
The precedence of operations: ** = ☆ > * = / = % > + = - = ◎。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 3 ☆ 4
Please fill your final answer in \boxed{}. | {
"game_data": {
"answer": "19",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ☆ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null,
"num_of_numbers": null,
"num_symbols": 2,
"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 15615552,
"simplified_expr": "( 4 + 4 * 3 + 3)",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": {
"associativity": "left",
"conditions": [
{
"condition": "x和y都是偶数",
"operation": " y - 4 - x - x"
}
],
"default_operation": " y - x + y",
"precedence": 1
},
"☆": {
"associativity": "left",
"conditions": [],
"default_operation": " y + y * x + x",
"precedence": 3
},
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "75e2e3da-f5a8-4af7-9aef-c6b34ffb49cc"
},
"question": "Define ◎, the rules are as follows:\nwhen x and y are both even, x ◎ y = y - 4 - x - x;\notherwise, x ◎ y = y - x + y.\nand ☆, the rules are as follows:\non the real number field, x ☆ y = y + y * x + x.\nThe precedence of operations: ** = ☆ > * = / = % > + = - = ◎。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 3 ☆ 4\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
"closing_sequence": null,
"expression": "3 ☆ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null,
"num_of_numbers": null,
"num_symbols": 2,
"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 15615552,
"simplified_expr": "( 4 + 4 * 3 + 3)",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": {
"associativity": "left",
"conditions": [
{
"condition": "x和y都是偶数",
"operation": " y - 4 - x - x"
}
],
"default_operation": " y - x + y",
"precedence": 1
},
"☆": {
"associativity": "left",
"conditions": [],
"default_operation": " y + y * x + x",
"precedence": 3
},
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "75e2e3da-f5a8-4af7-9aef-c6b34ffb49cc"
},
"seed": 15615552,
"task_id": 215615552,
"task_type": "operation"
} |
logic-v2 | Define ⊗, the rules are as follows:
on the real number field, x ⊗ y = (y / x) + x - y - 5.
and ◇, the rules are as follows:
on the real number field, x ◇ y = y * abs(x).
and ♢, the rules are as follows:
when x is a multiple of 5, x ♢ y = x / x + y - y + x;
otherwise, x ♢ y = y - x ◇ y.
The precedence of operations: ◇ > ** = ⊗ = ♢ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 9 ♢ 5 ◇ 4
Please fill your final answer in \boxed{}. | {
"game_data": {
"answer": "-160",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ♢ 5 ◇ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
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"n_types": null,
"nesting_depth": null,
"num_of_numbers": null,
"num_symbols": 3,
"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 7501959,
"simplified_expr": "((((4 * abs(5))) - (( ((4 * abs(5))) * abs(9)))))",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": {
"associativity": "left",
"conditions": [],
"default_operation": " (y / x) + x - y - 5",
"precedence": 3
},
"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": {
"associativity": "left",
"conditions": [],
"default_operation": " y * abs(x)",
"precedence": 4
},
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": {
"associativity": "left",
"conditions": [
{
"condition": "x是5的倍数",
"operation": " x / x + y - y + x"
}
],
"default_operation": " y - x ◇ y",
"precedence": 3
}
},
"target": null,
"total_length": null,
"trace_id": "9b8d9cd9-8a8f-4bb6-bc9c-94f6715b9e71"
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"question": "Define ⊗, the rules are as follows:\non the real number field, x ⊗ y = (y / x) + x - y - 5.\nand ◇, the rules are as follows:\non the real number field, x ◇ y = y * abs(x).\nand ♢, the rules are as follows:\nwhen x is a multiple of 5, x ♢ y = x / x + y - y + x;\notherwise, x ♢ y = y - x ◇ y.\nThe precedence of operations: ◇ > ** = ⊗ = ♢ > * = / = % > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 9 ♢ 5 ◇ 4\nPlease fill your final answer in \\boxed{}."
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logic-v2 | 定义 △，规则如下：
当x是5的倍数时，x △ y = x - (2 + y * x - x)；
其他情况下，x △ y = abs(y) / y - x。
运算优先级：** > * = / = % > + = - = △。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 + 2 △ 10
请将最终答案填入\boxed{}中。 | {
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"question": "定义 △，规则如下：\n当x是5的倍数时，x △ y = x - (2 + y * x - x)；\n其他情况下，x △ y = abs(y) / y - x。\n运算优先级：** > * = / = % > + = - = △。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 10 + 2 △ 10\n请将最终答案填入\\boxed{}中。"
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logic-v2 | Define ♡, the rules are as follows:
when x is less than y, x ♡ y = y + x - x + x;
otherwise, x ♡ y = (x / y * y).
and ⊗, the rules are as follows:
when the sum of x and y is even, x ⊗ y = x ♡ 5 - y;
otherwise, x ⊗ y = y / x + y - x.
The precedence of operations: ** > * = / = % > + = - = ♡ = ⊗。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 9 ♡ 1 ⊗ 4
Please fill your final answer in \boxed{}. | {
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"question": "Define ♡, the rules are as follows:\nwhen x is less than y, x ♡ y = y + x - x + x;\notherwise, x ♡ y = (x / y * y).\nand ⊗, the rules are as follows:\nwhen the sum of x and y is even, x ⊗ y = x ♡ 5 - y;\notherwise, x ⊗ y = y / x + y - x.\nThe precedence of operations: ** > * = / = % > + = - = ♡ = ⊗。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 9 ♡ 1 ⊗ 4\nPlease fill your final answer in \\boxed{}."
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logic-v2 | 定义 △，规则如下：
当x大于y时，x △ y = x - y * abs(x)；
其他情况下，x △ y = x / y。
运算优先级：** > * = / = % > + = - = △。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8
请将最终答案填入\boxed{}中。 | {
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logic-v2 | 定义 ☆，规则如下：
实数域上，x ☆ y = y * x - x - x。
和 ◎，规则如下：
实数域上，x ◎ y = y ☆ x + x。
运算优先级：** = ☆ > * = / = % = ◎ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 ◎ 7 ☆ 4 ☆ 5
请将最终答案填入\boxed{}中。 | {
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"question": "定义 ☆，规则如下：\n实数域上，x ☆ y = y * x - x - x。\n和 ◎，规则如下：\n实数域上，x ◎ y = y ☆ x + x。\n运算优先级：** = ☆ > * = / = % = ◎ > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 8 ◎ 7 ☆ 4 ☆ 5\n请将最终答案填入\\boxed{}中。"
},
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logic-v2 | Define ⊙, the rules are as follows:
on the real number field, x ⊙ y = 1 - (x * y) - 4.
and ♢, the rules are as follows:
on the real number field, x ♢ y = x / y - x.
and △, the rules are as follows:
when y is a multiple of 3, x △ y = x - x * y;
otherwise, x △ y = abs(2 * x * y) - x.
The precedence of operations: ** = ⊙ > * = / = % = ♢ > + = - = △。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 7 ⊙ 6 △ 6 ♢ 5
Please fill your final answer in \boxed{}. | {
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},
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logic-v2 | Define ⊕, the rules are as follows:
on the real number field, x ⊕ y = y * y + x - x.
and ▽, the rules are as follows:
when x is greater than y, x ▽ y = x / x - y;
otherwise, x ▽ y = y / y - y - abs(x).
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = 4 + x + y ▽ 5.
The precedence of operations: ⊕ > ** = ⊗ > * = / = % = ▽ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 9 ▽ 2 ⊗ 7
Please fill your final answer in \boxed{}. | {
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"⊗": {
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"conditions": [],
"default_operation": " 4 + x + y ▽ 5",
"precedence": 3
},
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"▽": {
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"conditions": [
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"condition": "x大于y",
"operation": " x / x - y"
}
],
"default_operation": " y / y - y - abs(x)",
"precedence": 2
},
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
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"question": "Define ⊕, the rules are as follows:\non the real number field, x ⊕ y = y * y + x - x.\nand ▽, the rules are as follows:\nwhen x is greater than y, x ▽ y = x / x - y;\notherwise, x ▽ y = y / y - y - abs(x).\nand ⊗, the rules are as follows:\non the real number field, x ⊗ y = 4 + x + y ▽ 5.\nThe precedence of operations: ⊕ > ** = ⊗ > * = / = % = ▽ > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 9 ▽ 2 ⊗ 7\nPlease fill your final answer in \\boxed{}."
},
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"seed": 377678,
"simplified_expr": "( (((((4 + 2)) + (( 7 / 7 - 5))))) / (((((4 + 2)) + (( 7 / 7 - 5))))) - (((((4 + 2)) + (( 7 / 7 - 5))))) - abs(9))",
"solutions_count": null,
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"seed": 377678,
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logic-v2 | Define ◎, the rules are as follows:
on the real number field, x ◎ y = y * y + y - x.
and ♡, the rules are as follows:
on the real number field, x ♡ y = (x) * y - x - y.
The precedence of operations: ◎ > ** > * = / = % = ♡ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 2 ◎ 6 ♡ 9 ♡ 1
Please fill your final answer in \boxed{}. | {
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"conditions": [],
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"♢": null
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"target": null,
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"question": "Define ◎, the rules are as follows:\non the real number field, x ◎ y = y * y + y - x.\nand ♡, the rules are as follows:\non the real number field, x ♡ y = (x) * y - x - y.\nThe precedence of operations: ◎ > ** > * = / = % = ♡ > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 2 ◎ 6 ♡ 9 ♡ 1\nPlease fill your final answer in \\boxed{}."
},
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"simplified_expr": "( ((( ((( 6 * 6 + 6 - 2))) * 9 - (( 6 * 6 + 6 - 2)) - 9))) * 1 - (( ((( 6 * 6 + 6 - 2))) * 9 - (( 6 * 6 + 6 - 2)) - 9)) - 1)",
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"♡": {
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"conditions": [],
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"precedence": 2
},
"♢": null
},
"target": null,
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},
"seed": 62765705,
"task_id": 262765705,
"task_type": "operation"
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logic-v2 | Define ◇, the rules are as follows:
when x is a multiple of 5, x ◇ y = 2 + y - x / 4;
otherwise, x ◇ y = x + 3 * 1 * y / y.
The precedence of operations: ** = ◇ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 3 ◇ 4 % 8 * 8
Please fill your final answer in \boxed{}. | {
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"question": "Define ◇, the rules are as follows:\nwhen x is a multiple of 5, x ◇ y = 2 + y - x / 4;\notherwise, x ◇ y = x + 3 * 1 * y / y.\nThe precedence of operations: ** = ◇ > * = / = % > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 3 ◇ 4 % 8 * 8\nPlease fill your final answer in \\boxed{}."
},
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"expression": "3 ◇ 4 % 8 * 8",
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"seed": 83731405,
"simplified_expr": "((((( 3 + 3 * 1 * 4 / 4)) % 8)) * 8)",
"solutions_count": null,
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"⊗": null,
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"△": null,
"▽": null,
"◇": {
"associativity": "left",
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},
"seed": 83731405,
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"task_type": "operation"
} |
logic-v2 | 定义 ♢，规则如下：
当x和y都是奇数时，x ♢ y = 5 / y - x；
其他情况下，x ♢ y = y / 2 - x。
和 △，规则如下：
当y是偶数时，x △ y = x + y + x；
其他情况下，x △ y = (x * y)。
和 ◇，规则如下：
实数域上，x ◇ y = y * y + x。
运算优先级：♢ > ** > * = / = % = ◇ > + = - = △。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5 ♢ 1 △ 6 ◇ 9
请将最终答案填入\boxed{}中。 | {
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"☆": null,
"♡": null,
"♢": {
"associativity": "left",
"conditions": [
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"condition": "x和y都是奇数",
"operation": " 5 / y - x"
}
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"default_operation": " y / 2 - x",
"precedence": 5
}
},
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"question": "定义 ♢，规则如下：\n当x和y都是奇数时，x ♢ y = 5 / y - x；\n其他情况下，x ♢ y = y / 2 - x。\n和 △，规则如下：\n当y是偶数时，x △ y = x + y + x；\n其他情况下，x △ y = (x * y)。\n和 ◇，规则如下：\n实数域上，x ◇ y = y * y + x。\n运算优先级：♢ > ** > * = / = % = ◇ > + = - = △。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 5 ♢ 1 △ 6 ◇ 9\n请将最终答案填入\\boxed{}中。"
},
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"expression": "5 ♢ 1 △ 6 ◇ 9",
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"simplified_expr": "( ((( 5 / 1 - 5)) * (( 9 * 9 + 6))))",
"solutions_count": null,
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"⊙": null,
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"△": {
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"conditions": [
{
"condition": "y是偶数",
"operation": " x + y + x"
}
],
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},
"▽": null,
"◇": {
"associativity": "left",
"conditions": [],
"default_operation": " y * y + x",
"precedence": 2
},
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": {
"associativity": "left",
"conditions": [
{
"condition": "x和y都是奇数",
"operation": " 5 / y - x"
}
],
"default_operation": " y / 2 - x",
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}
},
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"seed": 31163380,
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"task_type": "operation"
} |
logic-v2 | Define ☆, the rules are as follows:
on the real number field, x ☆ y = x / y.
and ○, the rules are as follows:
when y is a multiple of 3, x ○ y = x + y * x;
otherwise, x ○ y = y - x + x.
The precedence of operations: ☆ > ** = ○ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 4 ○ 8
Please fill your final answer in \boxed{}. | {
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"answer": "8",
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"associativity": "left",
"conditions": [],
"default_operation": " x / y",
"precedence": 4
},
"♡": null,
"♢": null
},
"target": null,
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"question": "Define ☆, the rules are as follows:\non the real number field, x ☆ y = x / y.\nand ○, the rules are as follows:\nwhen y is a multiple of 3, x ○ y = x + y * x;\notherwise, x ○ y = y - x + x.\nThe precedence of operations: ☆ > ** = ○ > * = / = % > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 4 ○ 8\nPlease fill your final answer in \\boxed{}."
},
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"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 29219220,
"simplified_expr": "( 8 - 4 + 4)",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": {
"associativity": "left",
"conditions": [
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"condition": "y是3的倍数",
"operation": " x + y * x"
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],
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"precedence": 3
},
"◎": null,
"☆": {
"associativity": "left",
"conditions": [],
"default_operation": " x / y",
"precedence": 4
},
"♡": null,
"♢": null
},
"target": null,
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"trace_id": "ee0bfcc4-a98a-47d9-b1dd-a208a084f277"
},
"seed": 29219220,
"task_id": 229219220,
"task_type": "operation"
} |
logic-v2 | 定义 △，规则如下：
实数域上，x △ y = abs(x / x - x - y) + x。
运算优先级：** > * = / = % = △ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2
请将最终答案填入\boxed{}中。 | {
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"question": "定义 △，规则如下：\n实数域上，x △ y = abs(x / x - x - y) + x。\n运算优先级：** > * = / = % = △ > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 2\n请将最终答案填入\\boxed{}中。"
},
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"□": null,
"△": {
"associativity": "left",
"conditions": [],
"default_operation": " abs(x / x - x - y) + x",
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"○": null,
"◎": null,
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"♢": null
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logic-v2 | 定义 ◇，规则如下：
实数域上，x ◇ y = x * (y + y / 1)。
和 ☆，规则如下：
当x和y的和是偶数时，x ☆ y = y ** y + x * x + x；
其他情况下，x ☆ y = (x) * y。
和 ◎，规则如下：
当x和y的和是奇数时，x ◎ y = y - (y) * x + y ☆ y；
其他情况下，x ◎ y = y ◇ y ** x + x + x。
运算优先级：◎ > ** = ◇ > * = / = % = ☆ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 ☆ 7 ◇ 9
请将最终答案填入\boxed{}中。 | {
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"question": "定义 ◇，规则如下：\n实数域上，x ◇ y = x * (y + y / 1)。\n和 ☆，规则如下：\n当x和y的和是偶数时，x ☆ y = y ** y + x * x + x；\n其他情况下，x ☆ y = (x) * y。\n和 ◎，规则如下：\n当x和y的和是奇数时，x ◎ y = y - (y) * x + y ☆ y；\n其他情况下，x ◎ y = y ◇ y ** x + x + x。\n运算优先级：◎ > ** = ◇ > * = / = % = ☆ > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 10 ☆ 7 ◇ 9\n请将最终答案填入\\boxed{}中。"
},
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logic-v2 | 定义 ▽，规则如下：
当x是3的倍数时，x ▽ y = x + x - y * x；
其他情况下，x ▽ y = x - y - 2 / x。
运算优先级：** > * = / = % > + = - = ▽。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6
请将最终答案填入\boxed{}中。 | {
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logic-v2 | 定义 □，规则如下：
实数域上，x □ y = x * y + y / x。
和 △，规则如下：
实数域上，x △ y = (y ** x) - x □ y。
运算优先级：□ = △ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 □ 1 △ 8
请将最终答案填入\boxed{}中。 | {
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logic-v2 | 定义 □，规则如下：
当x小于y时，x □ y = x * y - y；
其他情况下，x □ y = x + y。
和 ○，规则如下：
实数域上，x ○ y = x □ y * 3。
运算优先级：** > * = / = % = □ > + = - = ○。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 + 2 □ 10 * 2 ○ 4
请将最终答案填入\boxed{}中。 | {
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},
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logic-v2 | 定义 ○，规则如下：
当y是5的倍数时，x ○ y = x + x / y - x；
其他情况下，x ○ y = abs(x + 2) / y * 1。
运算优先级：○ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8
请将最终答案填入\boxed{}中。 | {
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logic-v2 | Define ⊙, the rules are as follows:
when the sum of x and y is odd, x ⊙ y = x + x - y;
otherwise, x ⊙ y = y - y - x - x * x.
and ♡, the rules are as follows:
on the real number field, x ♡ y = abs(x - 2 + y).
and ○, the rules are as follows:
on the real number field, x ○ y = (x + y) ♡ y.
The precedence of operations: ○ > ** > * = / = % = ♡ > + = - = ⊙。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 10 ♡ 5 + 7 ○ 2 ⊙ 8
Please fill your final answer in \boxed{}. | {
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},
"♢": null
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logic-v2 | 定义 ⊙，规则如下：
当x是偶数时，x ⊙ y = y - y * x；
其他情况下，x ⊙ y = y * x ** x。
和 ☆，规则如下：
实数域上，x ☆ y = y ⊙ y * x。
和 ○，规则如下：
当x是奇数时，x ○ y = y ☆ y * x；
其他情况下，x ○ y = x + y * y。
运算优先级：○ > ⊙ > ** > * = / = % = ☆ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 ○ 8 ☆ 4 + 5 ⊙ 5
请将最终答案填入\boxed{}中。 | {
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"question": "定义 ⊙，规则如下：\n当x是偶数时，x ⊙ y = y - y * x；\n其他情况下，x ⊙ y = y * x ** x。\n和 ☆，规则如下：\n实数域上，x ☆ y = y ⊙ y * x。\n和 ○，规则如下：\n当x是奇数时，x ○ y = y ☆ y * x；\n其他情况下，x ○ y = x + y * y。\n运算优先级：○ > ⊙ > ** > * = / = % = ☆ > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 3 ○ 8 ☆ 4 + 5 ⊙ 5\n请将最终答案填入\\boxed{}中。"
},
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logic-v2 | 定义 ♡，规则如下：
实数域上，x ♡ y = (4 + y + x)。
和 ○，规则如下：
当x小于y时，x ○ y = x / y；
其他情况下，x ○ y = y - x - abs(x + 5)。
运算优先级：♡ > ** > * = / = % = ○ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 ♡ 4 ○ 6
请将最终答案填入\boxed{}中。 | {
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"question": "定义 ♡，规则如下：\n实数域上，x ♡ y = (4 + y + x)。\n和 ○，规则如下：\n当x小于y时，x ○ y = x / y；\n其他情况下，x ○ y = y - x - abs(x + 5)。\n运算优先级：♡ > ** > * = / = % = ○ > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 3 ♡ 4 ○ 6\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
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"operators": null,
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"seed": 95392141,
"simplified_expr": "( 6 - (( (4 + 4 + 3))) - abs((( (4 + 4 + 3))) + 5))",
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"conditions": [],
"default_operation": " (4 + y + x)",
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"♢": null
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"seed": 95392141,
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logic-v2 | Define ◎, the rules are as follows:
when x is even, x ◎ y = x * y - y ** 5;
otherwise, x ◎ y = y * 1 / y / x.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = x * y + x ◎ y.
The precedence of operations: ◎ > ** = ⊗ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 2 ⊗ 2
Please fill your final answer in \boxed{}. | {
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"operation": " x * y - y ** 5"
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"☆": null,
"♡": null,
"♢": null
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"trace_id": "39ae90bc-a7d3-4b8e-aef3-a6f543512124"
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"question": "Define ◎, the rules are as follows:\nwhen x is even, x ◎ y = x * y - y ** 5;\notherwise, x ◎ y = y * 1 / y / x.\nand ⊗, the rules are as follows:\non the real number field, x ⊗ y = x * y + x ◎ y.\nThe precedence of operations: ◎ > ** = ⊗ > * = / = % > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 2 ⊗ 2\nPlease fill your final answer in \\boxed{}."
},
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"seed": 62279925,
"simplified_expr": "((((2 * 2)) + (( 2 * 2 - 2 ** 5))))",
"solutions_count": null,
"symbol_definitions": {
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"○": null,
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"conditions": [
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"operation": " x * y - y ** 5"
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],
"default_operation": " y * 1 / y / x",
"precedence": 4
},
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "39ae90bc-a7d3-4b8e-aef3-a6f543512124"
},
"seed": 62279925,
"task_id": 262279925,
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} |
logic-v2 | Define ⊙, the rules are as follows:
on the real number field, x ⊙ y = (x * y * 4).
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = (x ⊙ x) + y.
and ♡, the rules are as follows:
when y is a multiple of 5, x ♡ y = y + x - y;
otherwise, x ♡ y = x + (x + y).
The precedence of operations: ♡ > ⊙ = ⊗ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 9 ⊗ 2 ♡ 3
Please fill your final answer in \boxed{}. | {
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"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": {
"associativity": "left",
"conditions": [
{
"condition": "y是5的倍数",
"operation": " y + x - y"
}
],
"default_operation": " x + (x + y)",
"precedence": 5
},
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "dc37f4ee-64a9-407b-ad2e-cc31e46a1b04"
},
"question": "Define ⊙, the rules are as follows:\non the real number field, x ⊙ y = (x * y * 4).\nand ⊗, the rules are as follows:\non the real number field, x ⊗ y = (x ⊙ x) + y.\nand ♡, the rules are as follows:\nwhen y is a multiple of 5, x ♡ y = y + x - y;\notherwise, x ♡ y = x + (x + y).\nThe precedence of operations: ♡ > ⊙ = ⊗ > ** > * = / = % > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 9 ⊗ 2 ♡ 3\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
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"expression": "9 ⊗ 2 ♡ 3",
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"numbers": null,
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"seed": 95786152,
"simplified_expr": "(((( (9 * 9 * 4))) + ((2 + ((2 + 3))))))",
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},
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"conditions": [],
"default_operation": " (x * y * 4)",
"precedence": 4
},
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": {
"associativity": "left",
"conditions": [
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"condition": "y是5的倍数",
"operation": " y + x - y"
}
],
"default_operation": " x + (x + y)",
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},
"♢": null
},
"target": null,
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},
"seed": 95786152,
"task_id": 295786152,
"task_type": "operation"
} |
logic-v2 | Define ♡, the rules are as follows:
when x is odd, x ♡ y = 5 * x * y;
otherwise, x ♡ y = 2 * y + x.
and ▽, the rules are as follows:
on the real number field, x ▽ y = x + y - y.
The precedence of operations: ** = ▽ > * = / = % = ♡ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 4 ▽ 7
Please fill your final answer in \boxed{}. | {
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"operation": " 5 * x * y"
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"default_operation": " 2 * y + x",
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"♢": null
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"target": null,
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"question": "Define ♡, the rules are as follows:\nwhen x is odd, x ♡ y = 5 * x * y;\notherwise, x ♡ y = 2 * y + x.\nand ▽, the rules are as follows:\non the real number field, x ▽ y = x + y - y.\nThe precedence of operations: ** = ▽ > * = / = % = ♡ > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 4 ▽ 7\nPlease fill your final answer in \\boxed{}."
},
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"default_operation": " x + y - y",
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"○": null,
"◎": null,
"☆": null,
"♡": {
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],
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logic-v2 | 定义 ♢，规则如下：
当y是3的倍数时，x ♢ y = y + x - x；
其他情况下，x ♢ y = y + x * x。
和 ⊗，规则如下：
当x和y的和是偶数时，x ⊗ y = x ♢ y；
其他情况下，x ⊗ y = y * x ♢ y。
和 ⊙，规则如下：
当y是3的倍数时，x ⊙ y = y ♢ x；
其他情况下，x ⊙ y = x / x / y。
运算优先级：** = ♢ > * = / = % = ⊗ > + = - = ⊙。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 ♢ 6 ⊙ 10
请将最终答案填入\boxed{}中。 | {
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"△": null,
"▽": null,
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"◎": null,
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"question": "定义 ♢，规则如下：\n当y是3的倍数时，x ♢ y = y + x - x；\n其他情况下，x ♢ y = y + x * x。\n和 ⊗，规则如下：\n当x和y的和是偶数时，x ⊗ y = x ♢ y；\n其他情况下，x ⊗ y = y * x ♢ y。\n和 ⊙，规则如下：\n当y是3的倍数时，x ⊙ y = y ♢ x；\n其他情况下，x ⊙ y = x / x / y。\n运算优先级：** = ♢ > * = / = % = ⊗ > + = - = ⊙。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 3 ♢ 6 ⊙ 10\n请将最终答案填入\\boxed{}中。"
},
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"operation": " x ♢ y"
}
],
"default_operation": " y * x ♢ y",
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},
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],
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}
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logic-v2 | 定义 ⊕，规则如下：
实数域上，x ⊕ y = x * y / x。
和 ▽，规则如下：
实数域上，x ▽ y = x + 4 * x - y。
和 ♢，规则如下：
实数域上，x ♢ y = x / y ⊕ x。
运算优先级：▽ = ♢ > ** > * = / = % > + = - = ⊕。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 ♢ 3 ⊕ 9 ▽ 3
请将最终答案填入\boxed{}中。 | {
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logic-v2 | 定义 ▽，规则如下：
当x等于y时，x ▽ y = 5 + y - abs(x) * 5；
其他情况下，x ▽ y = x * y * x * 2。
运算优先级：** = ▽ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5
请将最终答案填入\boxed{}中。 | {
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},
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logic-v2 | 定义 ⊗，规则如下：
实数域上，x ⊗ y = y - y - x。
和 ☆，规则如下：
当x小于y时，x ☆ y = y + x；
其他情况下，x ☆ y = abs(y * x - y)。
和 □，规则如下：
实数域上，x □ y = y * x + x。
运算优先级：☆ > ⊗ > ** > * = / = % > + = - = □。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 □ 9 ⊗ 10 ☆ 1
请将最终答案填入\boxed{}中。 | {
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"question": "定义 ⊗，规则如下：\n实数域上，x ⊗ y = y - y - x。\n和 ☆，规则如下：\n当x小于y时，x ☆ y = y + x；\n其他情况下，x ☆ y = abs(y * x - y)。\n和 □，规则如下：\n实数域上，x □ y = y * x + x。\n运算优先级：☆ > ⊗ > ** > * = / = % > + = - = □。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 8 □ 9 ⊗ 10 ☆ 1\n请将最终答案填入\\boxed{}中。"
},
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logic-v2 | Define ▽, the rules are as follows:
on the real number field, x ▽ y = y * y / x - y + 5.
and ♢, the rules are as follows:
when y is a multiple of 3, x ♢ y = 4 ▽ y * y - y + x;
otherwise, x ♢ y = y / y * y / y + x.
The precedence of operations: ** > * = / = % = ♢ > + = - = ▽。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 7 ▽ 4 ▽ 1 ♢ 1 ♢ 2
Please fill your final answer in \boxed{}. | {
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logic-v2 | 定义 ⊗，规则如下：
实数域上，x ⊗ y = (y / x) * y。
和 △，规则如下：
实数域上，x △ y = y / x - x。
和 □，规则如下：
实数域上，x □ y = y + x + y。
运算优先级：⊗ > ** = □ > * = / = % > + = - = △。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 △ 9 ⊗ 10 □ 7
请将最终答案填入\boxed{}中。 | {
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logic-v2 | 定义 ☆，规则如下：
当y是5的倍数时，x ☆ y = y * x + 2；
其他情况下，x ☆ y = y + (x) / y。
和 ♢，规则如下：
当x是偶数时，x ♢ y = y * x；
其他情况下，x ♢ y = x / y - x。
运算优先级：☆ > ** > * = / = % > + = - = ♢。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 ☆ 1 ♢ 1 ♢ 10
请将最终答案填入\boxed{}中。 | {
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}
],
"default_operation": " x / y - x",
"precedence": 1
}
},
"target": null,
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"trace_id": "f8465213-5f0a-498f-a7c8-12dd2106d50f"
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"question": "定义 ☆，规则如下：\n当y是5的倍数时，x ☆ y = y * x + 2；\n其他情况下，x ☆ y = y + (x) / y。\n和 ♢，规则如下：\n当x是偶数时，x ♢ y = y * x；\n其他情况下，x ♢ y = x / y - x。\n运算优先级：☆ > ** > * = / = % > + = - = ♢。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 2 ☆ 1 ♢ 1 ♢ 10\n请将最终答案填入\\boxed{}中。"
},
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logic-v2 | 定义 ⊕，规则如下：
实数域上，x ⊕ y = y * x - 1 * x + 2。
和 ◇，规则如下：
实数域上，x ◇ y = y ** y + y + x - y。
和 ○，规则如下：
当y是偶数时，x ○ y = y ⊕ x + 4 + x；
其他情况下，x ○ y = x * y - y / y。
运算优先级：◇ > ** = ⊕ > * = / = % > + = - = ○。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 ○ 4 ◇ 1
请将最终答案填入\boxed{}中。 | {
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"question": "定义 ⊕，规则如下：\n实数域上，x ⊕ y = y * x - 1 * x + 2。\n和 ◇，规则如下：\n实数域上，x ◇ y = y ** y + y + x - y。\n和 ○，规则如下：\n当y是偶数时，x ○ y = y ⊕ x + 4 + x；\n其他情况下，x ○ y = x * y - y / y。\n运算优先级：◇ > ** = ⊕ > * = / = % > + = - = ○。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 4 ○ 4 ◇ 1\n请将最终答案填入\\boxed{}中。"
},
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"precedence": 5
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"conditions": [
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"operation": " y ⊕ x + 4 + x"
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},
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logic-v2 | 定义 ○，规则如下：
实数域上，x ○ y = x ** x - y。
运算优先级：○ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "4",
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"gpt_response": "",
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"question": "定义 ○，规则如下：\n实数域上，x ○ y = x ** x - y。\n运算优先级：○ > ** > * = / = % > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 4\n请将最终答案填入\\boxed{}中。"
},
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logic-v2 | Define ⊗, the rules are as follows:
on the real number field, x ⊗ y = 2 + y * x.
and ○, the rules are as follows:
when x is greater than y, x ○ y = x / y ⊗ y;
otherwise, x ○ y = x ⊗ y - x.
and ⊙, the rules are as follows:
when x is greater than y, x ⊙ y = 3 - x * y;
otherwise, x ⊙ y = x * x - y.
The precedence of operations: ⊗ > ○ = ⊙ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 5 ○ 4 ⊗ 10 ⊙ 6 ** 1
Please fill your final answer in \boxed{}. | {
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"question": "Define ⊗, the rules are as follows:\non the real number field, x ⊗ y = 2 + y * x.\nand ○, the rules are as follows:\nwhen x is greater than y, x ○ y = x / y ⊗ y;\notherwise, x ○ y = x ⊗ y - x.\nand ⊙, the rules are as follows:\nwhen x is greater than y, x ⊙ y = 3 - x * y;\notherwise, x ⊙ y = x * x - y.\nThe precedence of operations: ⊗ > ○ = ⊙ > ** > * = / = % > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 5 ○ 4 ⊗ 10 ⊙ 6 ** 1\nPlease fill your final answer in \\boxed{}."
},
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"▽": null,
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}
],
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"precedence": 4
},
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"☆": null,
"♡": null,
"♢": null
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logic-v2 | 定义 ○，规则如下：
实数域上，x ○ y = x - y * x / 3。
运算优先级：○ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3
请将最终答案填入\boxed{}中。 | {
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},
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logic-v2 | 定义 ▽，规则如下：
实数域上，x ▽ y = y - x + 4 / y。
运算优先级：** = ▽ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3
请将最终答案填入\boxed{}中。 | {
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"answer": "3",
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},
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logic-v2 | 定义 □，规则如下：
当x是5的倍数时，x □ y = 1 * x * y；
其他情况下，x □ y = y * x - y。
和 ◇，规则如下：
实数域上，x ◇ y = y / 3 - x □ y。
运算优先级：** > * = / = % > + = - = □ = ◇。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 □ 7 / 10 □ 8 ◇ 4
请将最终答案填入\boxed{}中。 | {
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"question": "定义 □，规则如下：\n当x是5的倍数时，x □ y = 1 * x * y；\n其他情况下，x □ y = y * x - y。\n和 ◇，规则如下：\n实数域上，x ◇ y = y / 3 - x □ y。\n运算优先级：** > * = / = % > + = - = □ = ◇。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 1 □ 7 / 10 □ 8 ◇ 4\n请将最终答案填入\\boxed{}中。"
},
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logic-v2 | Define ⊕, the rules are as follows:
when y is odd, x ⊕ y = (x / y - x);
otherwise, x ⊕ y = (y - x) - y.
and □, the rules are as follows:
when y is a multiple of 3, x □ y = y + x ⊕ x ** x;
otherwise, x □ y = y ⊕ x * y + x.
and ◎, the rules are as follows:
when y is a multiple of 5, x ◎ y = x □ y + y + y;
otherwise, x ◎ y = x * y □ y.
The precedence of operations: □ > ** > * = / = % = ◎ > + = - = ⊕。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 6 □ 1 ⊕ 2 ◎ 8
Please fill your final answer in \boxed{}. | {
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"question": "Define ⊕, the rules are as follows:\nwhen y is odd, x ⊕ y = (x / y - x);\notherwise, x ⊕ y = (y - x) - y.\nand □, the rules are as follows:\nwhen y is a multiple of 3, x □ y = y + x ⊕ x ** x;\notherwise, x □ y = y ⊕ x * y + x.\nand ◎, the rules are as follows:\nwhen y is a multiple of 5, x ◎ y = x □ y + y + y;\notherwise, x ◎ y = x * y □ y.\nThe precedence of operations: □ > ** > * = / = % = ◎ > + = - = ⊕。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 6 □ 1 ⊕ 2 ◎ 8\nPlease fill your final answer in \\boxed{}."
},
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"simplified_expr": "( ((((2 * ((((( (((8 * 8)) - 8) - ((8 * 8)))) + 8)))))) - ((((( (((6 * 1)) - 1) - ((6 * 1)))) + 6)))) - (((2 * ((((( (((8 * 8)) - 8) - ((8 * 8)))) + 8)))))))",
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logic-v2 | 定义 ○，规则如下：
实数域上，x ○ y = x - y * y。
运算优先级：○ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7 ○ 10
请将最终答案填入\boxed{}中。 | {
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},
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logic-v2 | 定义 ○，规则如下：
当x和y都是奇数时，x ○ y = x * y + x + y；
其他情况下，x ○ y = (y + y - y + x)。
运算优先级：** > * = / = % > + = - = ○。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 ** 1 % 2 ○ 9
请将最终答案填入\boxed{}中。 | {
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"question": "定义 ○，规则如下：\n当x和y都是奇数时，x ○ y = x * y + x + y；\n其他情况下，x ○ y = (y + y - y + x)。\n运算优先级：** > * = / = % > + = - = ○。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 6 ** 1 % 2 ○ 9\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
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logic-v2 | Define ♡, the rules are as follows:
when the sum of x and y is odd, x ♡ y = (5 + y + x + 3);
otherwise, x ♡ y = abs(y + x).
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = x - x / y + x.
The precedence of operations: ⊗ > ♡ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 4 ♡ 2 ⊗ 4
Please fill your final answer in \boxed{}. | {
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"operation": " (5 + y + x + 3)"
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],
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},
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "52981085-87b3-4870-bf10-c774e982f824"
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"question": "Define ♡, the rules are as follows:\nwhen the sum of x and y is odd, x ♡ y = (5 + y + x + 3);\notherwise, x ♡ y = abs(y + x).\nand ⊗, the rules are as follows:\non the real number field, x ⊗ y = x - x / y + x.\nThe precedence of operations: ⊗ > ♡ > ** > * = / = % > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 4 ♡ 2 ⊗ 4\nPlease fill your final answer in \\boxed{}."
},
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],
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},
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},
"seed": 19512783,
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} |
logic-v2 | 定义 □，规则如下：
实数域上，x □ y = y - (x * x)。
和 ♡，规则如下：
实数域上，x ♡ y = x - x - y。
运算优先级：** = □ > * = / = % = ♡ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 □ 3 ♡ 2 ** 4 * 7
请将最终答案填入\boxed{}中。 | {
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"target": null,
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"question": "定义 □，规则如下：\n实数域上，x □ y = y - (x * x)。\n和 ♡，规则如下：\n实数域上，x ♡ y = x - x - y。\n运算优先级：** = □ > * = / = % = ♡ > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 1 □ 3 ♡ 2 ** 4 * 7\n请将最终答案填入\\boxed{}中。"
},
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},
"seed": 44697288,
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} |
logic-v2 | Define ◎, the rules are as follows:
when y is odd, x ◎ y = 1 / y * x ** x;
otherwise, x ◎ y = x - y * y - x - y.
and ◇, the rules are as follows:
on the real number field, x ◇ y = x - y / x / x.
and △, the rules are as follows:
when y is a multiple of 5, x △ y = y ◇ 2 * x * 4;
otherwise, x △ y = x * x ** y + x / 5.
The precedence of operations: △ > ◇ > ** > * = / = % > + = - = ◎。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 5 ◎ 6 △ 2
Please fill your final answer in \boxed{}. | {
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"conditions": [
{
"condition": "y是奇数",
"operation": " 1 / y * x ** x"
}
],
"default_operation": " x - y * y - x - y",
"precedence": 1
},
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "ccea021d-c4e1-4d47-8e35-ff77203337cc"
},
"question": "Define ◎, the rules are as follows:\nwhen y is odd, x ◎ y = 1 / y * x ** x;\notherwise, x ◎ y = x - y * y - x - y.\nand ◇, the rules are as follows:\non the real number field, x ◇ y = x - y / x / x.\nand △, the rules are as follows:\nwhen y is a multiple of 5, x △ y = y ◇ 2 * x * 4;\notherwise, x △ y = x * x ** y + x / 5.\nThe precedence of operations: △ > ◇ > ** > * = / = % > + = - = ◎。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 5 ◎ 6 △ 2\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
"closing_sequence": null,
"expression": "5 ◎ 6 △ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null,
"num_of_numbers": null,
"num_symbols": 3,
"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 61016596,
"simplified_expr": "( 5 - (( 6 * 6 ** 2 + 6 / 5)) * (( 6 * 6 ** 2 + 6 / 5)) - 5 - (( 6 * 6 ** 2 + 6 / 5)))",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": {
"associativity": "left",
"conditions": [
{
"condition": "y是5的倍数",
"operation": " y ◇ 2 * x * 4"
}
],
"default_operation": " x * x ** y + x / 5",
"precedence": 5
},
"▽": null,
"◇": {
"associativity": "left",
"conditions": [],
"default_operation": " x - y / x / x",
"precedence": 4
},
"○": null,
"◎": {
"associativity": "left",
"conditions": [
{
"condition": "y是奇数",
"operation": " 1 / y * x ** x"
}
],
"default_operation": " x - y * y - x - y",
"precedence": 1
},
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "ccea021d-c4e1-4d47-8e35-ff77203337cc"
},
"seed": 61016596,
"task_id": 261016596,
"task_type": "operation"
} |
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