env stringclasses 1
value | prompt stringlengths 119 673 | extra dict |
|---|---|---|
logic-v2 | Define ♢, the rules are as follows:
when x and y are both even, x ♢ y = y - x - y;
otherwise, x ♢ y = (x - y - y).
and ◎, the rules are as follows:
on the real number field, x ◎ y = y * y ♢ x.
and △, the rules are as follows:
on the real number field, 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 ♢ 8 ◎ 8 △ 8
Please fill your final answer in \boxed{}. | {
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"simplified_expr": "( (( (8 + ((( 8 - ((8 * 8)) - 8)))))) - 2 - (( (8 + ((( 8 - ((8 * 8)) - 8)))))))",
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"◇": null,
"○": null,
"◎": {
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"conditions": [],
"default_operation": " y * y ♢ x",
"precedence": 4
},
"☆": null,
"♡": null,
"♢": {
"associativity": "left",
"conditions": [
{
"condition": "x和y都是偶数",
"operation": " y - x - y"
}
],
"default_operation": " (x - y - y)",
"precedence": 2
}
},
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"question": "Define ♢, the rules are as follows:\nwhen x and y are both even, x ♢ y = y - x - y;\notherwise, x ♢ y = (x - y - y).\nand ◎, the rules are as follows:\non the real number field, x ◎ y = y * y ♢ x.\nand △, the rules are as follows:\non the real number field, 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 ♢ 8 ◎ 8 △ 8\nPlease fill your final answer in \\boxed{}."
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"simplified_expr": "( (( (8 + ((( 8 - ((8 * 8)) - 8)))))) - 2 - (( (8 + ((( 8 - ((8 * 8)) - 8)))))))",
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"symbol_definitions": {
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"△": {
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"default_operation": " (y + x)",
"precedence": 4
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"▽": null,
"◇": null,
"○": null,
"◎": {
"associativity": "left",
"conditions": [],
"default_operation": " y * y ♢ x",
"precedence": 4
},
"☆": null,
"♡": null,
"♢": {
"associativity": "left",
"conditions": [
{
"condition": "x和y都是偶数",
"operation": " y - x - y"
}
],
"default_operation": " (x - y - y)",
"precedence": 2
}
},
"target": null,
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"trace_id": "d2b08991-7f57-4b50-8e8b-e886e1b15e12"
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"seed": 92318459,
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logic-v2 | Define ☆, the rules are as follows:
when y is odd, x ☆ y = y * y + y / x - 3;
otherwise, x ☆ y = x - y ** x.
and ♢, the rules are as follows:
when y is odd, x ♢ y = y + y + 3 + y / x;
otherwise, x ♢ y = 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: 2 ☆ 7 ♢ 8 - 10 / 2
Please fill your final answer in \boxed{}. | {
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"☆": {
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"operation": " y * y + y / x - 3"
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"default_operation": " x - y ** x",
"precedence": 5
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"♡": null,
"♢": {
"associativity": "left",
"conditions": [
{
"condition": "y是奇数",
"operation": " y + y + 3 + y / x"
}
],
"default_operation": " y * x - x + x + y",
"precedence": 2
}
},
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"question": "Define ☆, the rules are as follows:\nwhen y is odd, x ☆ y = y * y + y / x - 3;\notherwise, x ☆ y = x - y ** x.\nand ♢, the rules are as follows:\nwhen y is odd, x ♢ y = y + y + 3 + y / x;\notherwise, x ♢ y = 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: 2 ☆ 7 ♢ 8 - 10 / 2\nPlease fill your final answer in \\boxed{}."
},
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"expression": "2 ☆ 7 ♢ 8 - 10 / 2",
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"operators": null,
"question_sequence": null,
"seed": 37730550,
"simplified_expr": "((( 8 * (( 7 * 7 + 7 / 2 - 3)) - (( 7 * 7 + 7 / 2 - 3)) + (( 7 * 7 + 7 / 2 - 3)) + 8)) - ((10 / 2)))",
"solutions_count": null,
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"○": null,
"◎": null,
"☆": {
"associativity": "left",
"conditions": [
{
"condition": "y是奇数",
"operation": " y * y + y / x - 3"
}
],
"default_operation": " x - y ** x",
"precedence": 5
},
"♡": null,
"♢": {
"associativity": "left",
"conditions": [
{
"condition": "y是奇数",
"operation": " y + y + 3 + y / x"
}
],
"default_operation": " y * x - x + x + y",
"precedence": 2
}
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"total_length": null,
"trace_id": "bf387e4d-2bb7-42b4-8f05-5ba5ada4a138"
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"seed": 37730550,
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logic-v2 | 定义 ☆，规则如下：
当x是奇数时，x ☆ y = (x - y * y)；
其他情况下，x ☆ y = x - x - x * y。
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: 3 ▽ 4 ☆ 3
请将最终答案填入\boxed{}中。 | {
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"simplified_expr": "( (( 4 - 4 - 4 * 3)) - 3 + 3 * (( 4 - 4 - 4 * 3)))",
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"default_operation": " x - x - x * y",
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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是奇数时，x ☆ y = (x - y * y)；\n其他情况下，x ☆ y = x - x - x * y。\n和 ▽，规则如下：\n实数域上，x ▽ y = 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 ▽ 4 ☆ 3\n请将最终答案填入\\boxed{}中。"
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"simplified_expr": "( (( 4 - 4 - 4 * 3)) - 3 + 3 * (( 4 - 4 - 4 * 3)))",
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"default_operation": " y - x + x * y",
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},
"◇": null,
"○": null,
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"☆": {
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"conditions": [
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"operation": " (x - y * y)"
}
],
"default_operation": " x - x - x * y",
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"♢": null
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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：
实数域上，x ♡ y = y * y ⊗ x + 4。
和 ◇，规则如下：
当x是5的倍数时，x ◇ y = x - y - y - x；
其他情况下，x ◇ y = y - 3 ⊗ 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: 6 ♡ 3 ◇ 4 ⊗ 2
请将最终答案填入\boxed{}中。 | {
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"simplified_expr": "((((((2 * 2)) - 4)) - (((( ((((((6 * 6)) - ((3 * 3)))) + 4)) * ((((((6 * 6)) - ((3 * 3)))) + 4)) - 3)) * ((((((6 * 6)) - ((3 * 3)))) + 4))))))",
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"○": null,
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"♢": null
},
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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实数域上，x ♡ y = y * y ⊗ x + 4。\n和 ◇，规则如下：\n当x是5的倍数时，x ◇ y = x - y - y - x；\n其他情况下，x ◇ y = y - 3 ⊗ 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: 6 ♡ 3 ◇ 4 ⊗ 2\n请将最终答案填入\\boxed{}中。"
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"simplified_expr": "((((((2 * 2)) - 4)) - (((( ((((((6 * 6)) - ((3 * 3)))) + 4)) * ((((((6 * 6)) - ((3 * 3)))) + 4)) - 3)) * ((((((6 * 6)) - ((3 * 3)))) + 4))))))",
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logic-v2 | Define ◇, 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: 2 ◇ 5
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y是5的倍数时，x ○ y = y + y + x * y；
其他情况下，x ○ y = 2 / x + 4 / y。
和 ⊙，规则如下：
当x大于y时，x ⊙ y = y / x + x * y；
其他情况下，x ⊙ y = y + x ** y。
和 ♢，规则如下：
实数域上，x ♢ y = x - y * 4。
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 ♢ 3 ○ 9 ⊙ 4
请将最终答案填入\boxed{}中。 | {
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"question": "定义 ○，规则如下：\n当y是5的倍数时，x ○ y = y + y + x * y；\n其他情况下，x ○ y = 2 / x + 4 / y。\n和 ⊙，规则如下：\n当x大于y时，x ⊙ y = y / x + 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 = x - y * 4。\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: 7 ♢ 3 ○ 9 ⊙ 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 x and y are both even, x ♡ y = y + x + y;
otherwise, x ♡ y = y + y * y + x.
and ♢, the rules are as follows:
when x is equal to y, x ♢ y = 4 * x + y ♡ x;
otherwise, 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: 2 ♢ 9
Please fill your final answer in \boxed{}. | {
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"operation": " y + x + y"
}
],
"default_operation": " y + y * y + x",
"precedence": 1
},
"♢": {
"associativity": "left",
"conditions": [
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"condition": "x等于y",
"operation": " 4 * x + y ♡ x"
}
],
"default_operation": " y ♡ y * x * x",
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}
},
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"question": "Define ♡, the rules are as follows:\nwhen x and y are both even, x ♡ y = y + x + y;\notherwise, x ♡ y = y + y * y + x.\nand ♢, the rules are as follows:\nwhen x is equal to y, x ♢ y = 4 * x + y ♡ x;\notherwise, 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: 2 ♢ 9\nPlease fill your final answer in \\boxed{}."
},
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"seed": 23917928,
"simplified_expr": "(( ((((9 * 2)) * 2)) + ((((9 * 2)) * 2)) * ((((9 * 2)) * 2)) + 9))",
"solutions_count": null,
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"operation": " y + x + y"
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"precedence": 1
},
"♢": {
"associativity": "left",
"conditions": [
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"condition": "x等于y",
"operation": " 4 * x + y ♡ x"
}
],
"default_operation": " y ♡ y * x * x",
"precedence": 4
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"seed": 23917928,
"task_id": 223917928,
"task_type": "operation"
} |
logic-v2 | Define ○, the rules are as follows:
when the sum of x and y is even, x ○ y = (x + x) / y;
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: 2 ○ 5 % 10
Please fill your final answer in \boxed{}. | {
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"seed": 12889835,
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"solutions_count": null,
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"□": null,
"△": null,
"▽": null,
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"○": {
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"default_operation": " x + y * x",
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},
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},
"target": null,
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"trace_id": "688a2ac4-95ca-4f8f-9c06-943a587db1ff"
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"question": "Define ○, the rules are as follows:\nwhen the sum of x and y is even, x ○ y = (x + x) / y;\notherwise, x ○ 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: 2 ○ 5 % 10\nPlease fill your final answer in \\boxed{}."
},
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"solutions_count": null,
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"▽": null,
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"○": {
"associativity": "left",
"conditions": [
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"operation": " (x + x) / y"
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],
"default_operation": " x + y * x",
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},
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
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"trace_id": "688a2ac4-95ca-4f8f-9c06-943a587db1ff"
},
"seed": 12889835,
"task_id": 212889835,
"task_type": "operation"
} |
logic-v2 | Define ☆, the rules are as follows:
on the real number field, x ☆ y = y - 5 / x - y + y.
and ◎, the rules are as follows:
on the real number field, x ◎ y = 2 + x + y + x.
and ◇, the rules are as follows:
on the real number field, x ◇ y = 4 * abs(y + 2 + 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 ◎ 5 ◇ 2
Please fill your final answer in \boxed{}. | {
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"answer": "60",
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"○": null,
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"associativity": "left",
"conditions": [],
"default_operation": " 2 + x + y + x",
"precedence": 2
},
"☆": {
"associativity": "left",
"conditions": [],
"default_operation": " y - 5 / x - y + y",
"precedence": 5
},
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "39d85ff4-90d2-4947-a209-358f291a98cf"
},
"question": "Define ☆, the rules are as follows:\non the real number field, x ☆ y = y - 5 / x - y + y.\nand ◎, the rules are as follows:\non the real number field, x ◎ y = 2 + x + y + x.\nand ◇, the rules are as follows:\non the real number field, x ◇ y = 4 * abs(y + 2 + 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 ◎ 5 ◇ 2\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
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"expression": "2 ◎ 5 ◇ 2",
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"seed": 118284,
"simplified_expr": "( 4 * abs(2 + 2 + (( 2 + 2 + 5 + 2))))",
"solutions_count": null,
"symbol_definitions": {
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"default_operation": " 4 * abs(y + 2 + x)",
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},
"○": null,
"◎": {
"associativity": "left",
"conditions": [],
"default_operation": " 2 + x + y + x",
"precedence": 2
},
"☆": {
"associativity": "left",
"conditions": [],
"default_operation": " y - 5 / x - y + y",
"precedence": 5
},
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "39d85ff4-90d2-4947-a209-358f291a98cf"
},
"seed": 118284,
"task_id": 200118284,
"task_type": "operation"
} |
logic-v2 | Define ◎, the rules are as follows:
on the real number field, x ◎ y = x - 5 + y - y.
and ○, the rules are as follows:
when the sum of x and y is odd, x ○ y = (3 * y - 4 - y) - x;
otherwise, x ○ y = x ◎ 2 - y * y ** x.
and ⊕, the rules are as follows:
on the real number field, 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: 6 ○ 8 ⊕ 1
Please fill your final answer in \boxed{}. | {
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"answer": "16385",
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"expression": "6 ○ 8 ⊕ 1",
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"solutions_count": null,
"symbol_definitions": {
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"△": null,
"▽": null,
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"conditions": [
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"condition": "x和y的和是奇数",
"operation": " (3 * y - 4 - y) - x"
}
],
"default_operation": " x ◎ 2 - y * y ** x",
"precedence": 2
},
"◎": {
"associativity": "left",
"conditions": [],
"default_operation": " x - 5 + y - y",
"precedence": 5
},
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
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"question": "Define ◎, the rules are as follows:\non the real number field, x ◎ y = x - 5 + y - y.\nand ○, the rules are as follows:\nwhen the sum of x and y is odd, x ○ y = (3 * y - 4 - y) - x;\notherwise, x ○ y = x ◎ 2 - y * y ** x.\nand ⊕, the rules are as follows:\non the real number field, 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: 6 ○ 8 ⊕ 1\nPlease fill your final answer in \\boxed{}."
},
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"expression": "6 ○ 8 ⊕ 1",
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"seed": 26199646,
"simplified_expr": "(((( 6 - 5 + 2 - 2)) - ((((((((1 - 5)) + 8)) - 8)) * ((((((((1 - 5)) + 8)) - 8)) ** 6))))))",
"solutions_count": null,
"symbol_definitions": {
"⊕": {
"associativity": "left",
"conditions": [],
"default_operation": " (y ◎ x)",
"precedence": 3
},
"⊗": null,
"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": {
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"conditions": [
{
"condition": "x和y的和是奇数",
"operation": " (3 * y - 4 - y) - x"
}
],
"default_operation": " x ◎ 2 - y * y ** x",
"precedence": 2
},
"◎": {
"associativity": "left",
"conditions": [],
"default_operation": " x - 5 + y - y",
"precedence": 5
},
"☆": null,
"♡": null,
"♢": null
},
"target": null,
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"trace_id": "f2f27ae5-5beb-4d8a-b814-18545d2a65d6"
},
"seed": 26199646,
"task_id": 226199646,
"task_type": "operation"
} |
logic-v2 | Define ◇, the rules are as follows:
on the real number field, x ◇ y = y + x + 4 / 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 ◇ 7
Please fill your final answer in \boxed{}. | {
"game_data": {
"answer": "16.571429",
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"gpt_response": "",
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"solutions_count": null,
"symbol_definitions": {
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"⊗": null,
"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": {
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"default_operation": " y + x + 4 / y",
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"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
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"question": "Define ◇, the rules are as follows:\non the real number field, x ◇ y = y + x + 4 / 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 ◇ 7\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
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"expression": "9 ◇ 7",
"fill_length": null,
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"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null,
"num_of_numbers": null,
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"solutions_count": null,
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"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": {
"associativity": "left",
"conditions": [],
"default_operation": " y + x + 4 / y",
"precedence": 5
},
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
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"trace_id": "a4ee9eb5-9062-4bd8-acac-dca4f2396ee5"
},
"seed": 16003036,
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} |
logic-v2 | Define ⊗, the rules are as follows:
when y is a multiple of 5, x ⊗ y = y ** y - x;
otherwise, x ⊗ y = y + x.
and ☆, the rules are as follows:
when x and y are both even, x ☆ y = x + x + y;
otherwise, x ☆ y = y / y * (x).
and ♢, the rules are as follows:
when y is odd, x ♢ y = abs(x + y);
otherwise, x ♢ y = y + 5 + 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: 5 / 8 ☆ 1 ⊗ 10 ♢ 1 / 7
Please fill your final answer in \boxed{}. | {
"game_data": {
"answer": "0.625",
"difficulty": 1,
"gpt_response": "",
"metadata": {
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"expression": "5 / 8 ☆ 1 ⊗ 10 ♢ 1 / 7",
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"simplified_expr": "( (((( abs((( 10 ** 10 - 1)) + 1))) / 7)) / (((( abs((( 10 ** 10 - 1)) + 1))) / 7)) * (((5 / 8))))",
"solutions_count": null,
"symbol_definitions": {
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],
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"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": {
"associativity": "left",
"conditions": [
{
"condition": "x和y都是偶数",
"operation": " x + x + y"
}
],
"default_operation": " y / y * (x)",
"precedence": 1
},
"♡": null,
"♢": {
"associativity": "left",
"conditions": [
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"operation": " abs(x + y)"
}
],
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}
},
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"trace_id": "f963ff14-d9f0-43df-be4f-98993c92dbb1"
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"question": "Define ⊗, the rules are as follows:\nwhen y is a multiple of 5, x ⊗ y = y ** y - x;\notherwise, x ⊗ y = y + x.\nand ☆, the rules are as follows:\nwhen x and y are both even, x ☆ y = x + x + y;\notherwise, x ☆ y = y / y * (x).\nand ♢, the rules are as follows:\nwhen y is odd, x ♢ y = abs(x + y);\notherwise, x ♢ y = y + 5 + 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: 5 / 8 ☆ 1 ⊗ 10 ♢ 1 / 7\nPlease fill your final answer in \\boxed{}."
},
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"simplified_expr": "( (((( abs((( 10 ** 10 - 1)) + 1))) / 7)) / (((( abs((( 10 ** 10 - 1)) + 1))) / 7)) * (((5 / 8))))",
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"condition": "x和y都是偶数",
"operation": " x + x + y"
}
],
"default_operation": " y / y * (x)",
"precedence": 1
},
"♡": null,
"♢": {
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"operation": " abs(x + y)"
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logic-v2 | 定义 ⊙，规则如下：
实数域上，x ⊙ y = (x + x) - x + y。
和 ♢，规则如下：
当x是5的倍数时，x ♢ y = x * y；
其他情况下，x ♢ y = y - (y + y) * x。
和 ◎，规则如下：
当y是偶数时，x ◎ y = y * x + y；
其他情况下，x ◎ y = x - 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: 4 * 4 ⊙ 9 ♢ 1 ◎ 7
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) - x + y。\n和 ♢，规则如下：\n当x是5的倍数时，x ♢ y = x * y；\n其他情况下，x ♢ y = y - (y + y) * x。\n和 ◎，规则如下：\n当y是偶数时，x ◎ y = y * x + y；\n其他情况下，x ◎ y = x - 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: 4 * 4 ⊙ 9 ♢ 1 ◎ 7\n请将最终答案填入\\boxed{}中。"
},
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"simplified_expr": "( (((4 * 4)) + ((4 * 4))) - ((4 * 4)) + (( (( 1 - (1 + 1) * 9)) - 7 ** (( 1 - (1 + 1) * 9)) + (( 1 - (1 + 1) * 9)))))",
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logic-v2 | 定义 ⊗，规则如下：
实数域上，x ⊗ y = 3 - x * y - x。
和 □，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 - y - 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: 9 ▽ 10 ⊗ 4 □ 9 ⊗ 1
请将最终答案填入\boxed{}中。 | {
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"conditions": [],
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"precedence": 3
},
"△": null,
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"associativity": "left",
"conditions": [],
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"○": null,
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"♡": null,
"♢": null
},
"target": null,
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"question": "定义 ⊗，规则如下：\n实数域上，x ⊗ y = 3 - x * y - x。\n和 □，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 - y - 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: 9 ▽ 10 ⊗ 4 □ 9 ⊗ 1\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
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"simplified_expr": "( 3 - (((9 + (((( 3 - ((((3 - ((((((((9 + ((((((3 - ((10 * 10)))) - 10)) ** 10)))) - 10)) - 5)) * 4)))) - ((((((9 + ((((((3 - ((10 * 10)))) - 10)) ** 10)))) - 10)) - 5)))) * ((((3 - ((((((((9 + ((((((3 - ((10 * 10)))) - 10)) ** 10)))) - 10)) - 5)) * 4)))) - ((((((9 + ((((((3 - ((10 * 10)))) - 10)) ** 10)))) - 10)) - 5)))) - ((((3 - ((((((((9 + ((((((3 - ((10 * 10)))) - 10)) ** 10)))) - 10)) - 5)) * 4)))) - ((((((9 + ((((((3 - ((10 * 10)))) - 10)) ** 10)))) - 10)) - 5)))))) ** ((((3 - ((((((((9 + ((((((3 - ((10 * 10)))) - 10)) ** 10)))) - 10)) - 5)) * 4)))) - ((((((9 + ((((((3 - ((10 * 10)))) - 10)) ** 10)))) - 10)) - 5))))))))) * 1 - (((9 + (((( 3 - ((((3 - ((((((((9 + ((((((3 - ((10 * 10)))) - 10)) ** 10)))) - 10)) - 5)) * 4)))) - ((((((9 + ((((((3 - ((10 * 10)))) - 10)) ** 10)))) - 10)) - 5)))) * ((((3 - ((((((((9 + ((((((3 - ((10 * 10)))) - 10)) ** 10)))) - 10)) - 5)) * 4)))) - ((((((9 + ((((((3 - ((10 * 10)))) - 10)) ** 10)))) - 10)) - 5)))) - ((((3 - ((((((((9 + ((((((3 - ((10 * 10)))) - 10)) ** 10)))) - 10)) - 5)) * 4)))) - ((((((9 + ((((((3 - ((10 * 10)))) - 10)) ** 10)))) - 10)) - 5)))))) ** ((((3 - ((((((((9 + ((((((3 - ((10 * 10)))) - 10)) ** 10)))) - 10)) - 5)) * 4)))) - ((((((9 + ((((((3 - ((10 * 10)))) - 10)) ** 10)))) - 10)) - 5))))))))))",
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"conditions": [],
"default_operation": " y + x ⊗ x ** x",
"precedence": 3
},
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"▽": {
"associativity": "left",
"conditions": [],
"default_operation": " y □ x - y - 5",
"precedence": 3
},
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} |
logic-v2 | Define ♢, the rules are as follows:
on the real number field, x ♢ y = x + 5 * (y * x * x).
and ◇, the rules are as follows:
when x is equal to y, x ◇ y = 4 + x + x ** x * y;
otherwise, x ◇ y = (y) / x.
and □, the rules are as follows:
when x is less than y, x □ y = x ** y - x;
otherwise, x □ y = x * 5 * 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 ♢ 2 □ 4 ◇ 8 % 4
Please fill your final answer in \boxed{}. | {
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},
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"default_operation": " x + 5 * (y * x * x)",
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}
},
"target": null,
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"question": "Define ♢, the rules are as follows:\non the real number field, x ♢ y = x + 5 * (y * x * x).\nand ◇, the rules are as follows:\nwhen x is equal to y, x ◇ y = 4 + x + x ** x * y;\notherwise, x ◇ y = (y) / x.\nand □, the rules are as follows:\nwhen x is less than y, x □ y = x ** y - x;\notherwise, x □ y = x * 5 * 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 ♢ 2 □ 4 ◇ 8 % 4\nPlease fill your final answer in \\boxed{}."
},
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},
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"▽": null,
"◇": {
"associativity": "left",
"conditions": [
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"operation": " 4 + x + x ** x * y"
}
],
"default_operation": " (y) / x",
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},
"○": null,
"◎": null,
"☆": null,
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"♢": {
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"default_operation": " x + 5 * (y * x * x)",
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}
},
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"seed": 72220482,
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logic-v2 | Define ▽, the rules are as follows:
when x is a multiple of 3, x ▽ y = abs(y ** y * y * x) * y;
otherwise, x ▽ y = x + x / 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: 3 / 10 - 10 ▽ 3
Please fill your final answer in \boxed{}. | {
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"♢": null
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},
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"solutions_count": null,
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"⊗": null,
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"▽": {
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"conditions": [
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"operation": " abs(y ** y * y * x) * y"
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"seed": 92168845,
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} |
logic-v2 | 定义 ◎，规则如下：
实数域上，x ◎ y = y - x / x * x - x。
和 ⊙，规则如下：
当x等于y时，x ⊙ y = x + y / y ◎ x * x；
其他情况下，x ⊙ y = y * y * y * abs(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: 7 ⊙ 4 ◎ 9 - 5 ⊙ 2
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 = (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: 4 + 1 ⊗ 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 = 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: 3 ◇ 8 ◇ 7 ◇ 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：
当x和y都是奇数时，x ♢ y = y - 5 + x；
其他情况下，x ♢ y = y + x + x。
和 ○，规则如下：
实数域上，x ○ y = abs(x + x) * y。
和 ⊗，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: 10 ⊗ 9 ○ 4 ♢ 10
请将最终答案填入\boxed{}中。 | {
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},
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"operation": " y - 5 + x"
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}
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logic-v2 | Define ⊕, the rules are as follows:
when x and y are both odd, x ⊕ y = x ** x ** y;
otherwise, x ⊕ y = y * x.
and ⊙, the rules are as follows:
when y is a multiple of 5, x ⊙ y = x - x / y;
otherwise, x ⊙ y = y + y + x.
and ○, the rules are as follows:
on the real number field, 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: 6 ⊙ 7 ○ 8 ⊕ 10
Please fill your final answer in \boxed{}. | {
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"♢": null
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"question": "Define ⊕, the rules are as follows:\nwhen x and y are both odd, x ⊕ y = x ** x ** y;\notherwise, x ⊕ y = y * x.\nand ⊙, the rules are as follows:\nwhen y is a multiple of 5, x ⊙ y = x - x / y;\notherwise, x ⊙ y = y + y + x.\nand ○, the rules are as follows:\non the real number field, 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: 6 ⊙ 7 ○ 8 ⊕ 10\nPlease fill your final answer in \\boxed{}."
},
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},
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"☆": null,
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logic-v2 | 定义 ◇，规则如下：
实数域上，x ◇ y = y * x - 5。
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: 7 ◇ 6 ◇ 4 + 5 ♡ 7
请将最终答案填入\boxed{}中。 | {
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"conditions": [],
"default_operation": " x + x - y",
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"♢": null
},
"target": null,
"total_length": null,
"trace_id": "b3214e9a-c79b-4b8a-94a1-b30add89ea72"
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"question": "定义 ◇，规则如下：\n实数域上，x ◇ y = y * x - 5。\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: 7 ◇ 6 ◇ 4 + 5 ♡ 7\n请将最终答案填入\\boxed{}中。"
},
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"solutions_count": 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 * x - x - y。
和 ◎，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 - 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: 5 ◎ 10 ◇ 2
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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 = 2 / 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 △ 7
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logic-v2 | 定义 ◎，规则如下：
当x和y都是偶数时，x ◎ y = x - y * y + (y)；
其他情况下，x ◎ y = x + y + y - y + x。
和 ♢，规则如下：
实数域上，x ♢ y = x + 3 / 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: 8 % 7 ◎ 2 ♢ 3
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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: 10 ▽ 8 * 2
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 + y；
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: 5 ☆ 10 % 6
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logic-v2 | 定义 ⊙，规则如下：
当x和y的和是奇数时，x ⊙ y = y - abs(x) * 5 - y；
其他情况下，x ⊙ y = x / y - x - x。
和 ♢，规则如下：
实数域上，x ♢ y = y + x。
和 ♡，规则如下：
当x等于y时，x ♡ y = y + x ♢ x；
其他情况下，x ♡ 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: 7 * 1 ⊙ 10 ♢ 2 ♡ 9
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logic-v2 | Define ⊙, the rules are as follows:
on the real number field, x ⊙ y = x + (x / y).
and ▽, the rules are as follows:
on the real number field, x ▽ y = x - y ⊙ (x).
and ◎, the rules are as follows:
when the sum of x and y is odd, x ◎ y = abs(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: 7 ◎ 3 ⊙ 5
Please 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 = y / x + x；
其他情况下，x ◇ 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: 1 % 5 % 3 ◇ 7
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 + y + x) - y.
and △, the rules are as follows:
when the sum of x and y is odd, x △ y = x / x + y ☆ x * x;
otherwise, x △ y = x * x - 1 + 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 △ 1
Please fill your final answer in \boxed{}. | {
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} |
logic-v2 | Define ⊙, the rules are as follows:
on the real number field, x ⊙ y = y - 2 - y * x - 3.
and ⊕, the rules are as follows:
when x is a multiple of 3, x ⊕ y = x + 5 + x - x + y;
otherwise, x ⊕ y = y ** y ⊙ x - y * x.
and ○, the rules are as follows:
on the real number field, x ○ y = 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: 3 ○ 3 ⊕ 5 ⊙ 1
Please fill your final answer in \boxed{}. | {
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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 = abs(x) * y；
其他情况下，x ♡ y = x * y。
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: 10 + 6 ♡ 5 □ 4
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 = x + x - y / x；
其他情况下，x □ y = x * y * abs(1 - y)。
和 ⊗，规则如下：
实数域上，x ⊗ y = x □ 2 + 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: 6 ⊗ 10
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 = 3 - x - 5 - x * y.
and ⊙, the rules are as follows:
when x is odd, x ⊙ y = y - x - x ♢ x + x;
otherwise, x ⊙ y = abs(x * y * y - y - y).
and ◎, the rules are as follows:
on the real number field, x ◎ y = (1 / 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: 8 ⊙ 1 ◎ 6 ♢ 4
Please fill your final answer in \boxed{}. | {
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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 = y + x；
其他情况下，x ◇ y = x * 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: 6 ◇ 8 % 4
请将最终答案填入\boxed{}中。 | {
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},
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"simplified_expr": "((( 6 * 6 / 8 - 8)) % 4)",
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logic-v2 | Define ♡, the rules are as follows:
on the real number field, x ♡ y = x - y * 3 + y.
and ◎, the rules are as follows:
on the real number field, x ◎ y = x + 3 * 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 ♡ 3 ◎ 10 ◎ 1 % 1
Please fill your final answer in \boxed{}. | {
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},
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"seed": 47766885,
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} |
logic-v2 | 定义 □，规则如下：
当y是奇数时，x □ y = x ** x * y + y；
其他情况下，x □ y = x - x + y + y。
和 ♡，规则如下：
当y是3的倍数时，x ♡ y = 4 * y - 1 □ x；
其他情况下，x ♡ y = x □ 3 * 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 - 3 □ 10 ♡ 4 + 8
请将最终答案填入\boxed{}中。 | {
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"conditions": [
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"question": "定义 □，规则如下：\n当y是奇数时，x □ y = x ** x * y + y；\n其他情况下，x □ y = x - x + y + y。\n和 ♡，规则如下：\n当y是3的倍数时，x ♡ y = 4 * y - 1 □ x；\n其他情况下，x ♡ y = x □ 3 * 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 - 3 □ 10 ♡ 4 + 8\n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小于y时，x ▽ y = abs(y) + x；
其他情况下，x ▽ y = (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: 10 ▽ 7
请将最终答案填入\boxed{}中。 | {
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"gpt_response": "",
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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 - y.
and ☆, the rules are as follows:
on the real number field, x ☆ y = x * x - y.
and ▽, the rules are as follows:
on the real number field, x ▽ y = x ** abs(y) - 4.
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 ⊕ 3 ▽ 1 ☆ 5
Please fill your final answer in \boxed{}. | {
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"precedence": 2
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"◇": null,
"○": null,
"◎": null,
"☆": {
"associativity": "left",
"conditions": [],
"default_operation": " x * x - y",
"precedence": 1
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"♡": null,
"♢": null
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"target": null,
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},
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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 * y)。
和 ⊕，规则如下：
当y是奇数时，x ⊕ y = x * x * y；
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: 10 ⊕ 6 ◎ 4
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 - x + x + x.
and ◇, the rules are as follows:
when y is a multiple of 5, x ◇ y = y ♢ x ** x - 1;
otherwise, x ◇ y = (y / x) - x * x.
and ⊙, the rules are as follows:
on the real number field, 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 - 7 ♢ 6 ◇ 6 ⊙ 5
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 - 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 △ 3 + 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 - 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 △ 3 + 5\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等于y时，x ⊗ y = x ** 4 - x + (y + 4)；
其他情况下，x ⊗ y = x + y + y - x。
和 □，规则如下：
实数域上，x □ y = y * y - 4 ⊗ x。
和 ♡，规则如下：
当x和y都是奇数时，x ♡ y = y + (x - y) + y - y；
其他情况下，x ♡ y = 5 - 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: 4 □ 3 ♡ 4 ⊗ 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等于y时，x ⊗ y = x ** 4 - x + (y + 4)；\n其他情况下，x ⊗ y = x + y + y - x。\n和 □，规则如下：\n实数域上，x □ y = y * y - 4 ⊗ x。\n和 ♡，规则如下：\n当x和y都是奇数时，x ♡ y = y + (x - y) + y - y；\n其他情况下，x ♡ y = 5 - 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: 4 □ 3 ♡ 4 ⊗ 3\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 = x + y + 1.
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: 10 ▽ 10 ♢ 10 % 9
Please fill your final answer in \boxed{}. | {
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logic-v2 | Define ⊙, the rules are as follows:
when x is a multiple of 3, x ⊙ y = 4 / y - x;
otherwise, x ⊙ y = abs(x / y).
and □, the rules are as follows:
when x is odd, x □ y = x ⊙ y;
otherwise, x □ y = x ⊙ y.
and ○, the rules are as follows:
when x is equal to y, x ○ y = x / y;
otherwise, 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: 4 □ 4 ⊙ 2
Please fill your final answer in \boxed{}. | {
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},
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},
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"question": "Define ⊙, the rules are as follows:\nwhen x is a multiple of 3, x ⊙ y = 4 / y - x;\notherwise, x ⊙ y = abs(x / y).\nand □, the rules are as follows:\nwhen x is odd, x □ y = x ⊙ y;\notherwise, x □ y = x ⊙ y.\nand ○, the rules are as follows:\nwhen x is equal to y, x ○ y = x / y;\notherwise, 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: 4 □ 4 ⊙ 2\nPlease fill your final answer in \\boxed{}."
},
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logic-v2 | Define ⊗, the rules are as follows:
on the real number field, x ⊗ y = x * y.
and ⊕, the rules are as follows:
when x is equal to y, x ⊕ y = x + y ⊗ 3;
otherwise, x ⊕ y = 2 / y - x.
and ▽, the rules are as follows:
on the real number field, x ▽ y = 1 - 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 ⊕ 3 ▽ 8 ⊗ 2
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 = x * y.\nand ⊕, the rules are as follows:\nwhen x is equal to y, x ⊕ y = x + y ⊗ 3;\notherwise, x ⊕ y = 2 / y - x.\nand ▽, the rules are as follows:\non the real number field, x ▽ y = 1 - 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 ⊕ 3 ▽ 8 ⊗ 2\nPlease fill your final answer in \\boxed{}."
},
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"simplified_expr": "( (( 2 / (( 1 - 3 - 8)) - 1)) * 2)",
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"precedence": 5
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"seed": 96994612,
"task_id": 296994612,
"task_type": "operation"
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logic-v2 | 定义 ▽，规则如下：
实数域上，x ▽ 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: 1
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小于y时，x □ y = y * y * x * x；
其他情况下，x □ y = x + x * abs(y + x)。
和 ☆，规则如下：
实数域上，x ☆ y = y - x - y。
和 △，规则如下：
当y是奇数时，x △ y = x + y + abs(x)；
其他情况下，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: 1 △ 9 ☆ 5 ☆ 9 □ 6
请将最终答案填入\boxed{}中。 | {
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"question": "定义 □，规则如下：\n当x小于y时，x □ y = y * y * x * x；\n其他情况下，x □ y = x + x * abs(y + x)。\n和 ☆，规则如下：\n实数域上，x ☆ y = y - x - y。\n和 △，规则如下：\n当y是奇数时，x △ y = x + y + abs(x)；\n其他情况下，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: 1 △ 9 ☆ 5 ☆ 9 □ 6\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和y的和是偶数时，x ♡ y = x - x - x - y + x；
其他情况下，x ♡ y = y - x * y - x - y。
和 ◇，规则如下：
实数域上，x ◇ y = y + x * 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: 6 + 4 ♡ 1 ◇ 4
请将最终答案填入\boxed{}中。 | {
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"operation": " x - x - x - y + x"
}
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"question": "定义 ♡，规则如下：\n当x和y的和是偶数时，x ♡ y = x - x - x - y + x；\n其他情况下，x ♡ y = y - x * y - x - y。\n和 ◇，规则如下：\n实数域上，x ◇ y = y + x * 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: 6 + 4 ♡ 1 ◇ 4\n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 = x - y - y * 3。
和 ⊙，规则如下：
当x是3的倍数时，x ⊙ y = x ◎ y - y + y；
其他情况下，x ⊙ y = x + 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: 7 ◎ 2
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 = y - y + (x) * y - y；
其他情况下，x □ y = y - y - x + y + y。
和 ⊗，规则如下：
当x是偶数时，x ⊗ y = (x - y) + x；
其他情况下，x ⊗ y = y + x + 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: 2 ⊗ 3
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 = x * 2 + y * x.
and ○, 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: 7 ○ 2 ☆ 5
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 + 5 + y。
和 ♢，规则如下：
当x和y的和是偶数时，x ♢ y = x ⊙ y - x；
其他情况下，x ♢ y = y * x ⊙ y。
和 ▽，规则如下：
实数域上，x ▽ y = x + abs(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: 10 - 4 ♢ 4 ▽ 4 ⊙ 6
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 = 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 ◇ 4 + 6 ◇ 8
Please fill your final answer in \boxed{}. | {
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logic-v2 | Define ◇, the rules are as follows:
when x is even, x ◇ y = 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
Please fill your final answer in \boxed{}. | {
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logic-v2 | 定义 ⊗，规则如下：
当x是3的倍数时，x ⊗ y = y - x / y + y + y；
其他情况下，x ⊗ y = y / (x) + y / x。
和 △，规则如下：
实数域上，x △ y = y - x - y - x * y。
和 ◇，规则如下：
实数域上，x ◇ y = y * 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: 2 ◇ 6 △ 8 ⊗ 9
请将最终答案填入\boxed{}中。 | {
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},
"▽": null,
"◇": {
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"conditions": [],
"default_operation": " y * y - x + y - y",
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},
"○": null,
"◎": null,
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"♢": null
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} |
logic-v2 | Define ♢, the rules are as follows:
when x is greater than y, x ♢ y = abs(2 + x + x * y);
otherwise, x ♢ y = x + y - y + x.
and ⊕, the rules are as follows:
when y is a multiple of 3, x ⊕ y = x - 5 + x * y;
otherwise, x ⊕ y = (x - y) * x.
and ♡, the rules are as follows:
on the real number field, 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: 7 ⊕ 4 ♡ 3 + 7 ♢ 9
Please fill your final answer in \boxed{}. | {
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logic-v2 | Define ⊕, the rules are as follows:
when x is a multiple of 5, x ⊕ y = x * x + y * y - x;
otherwise, x ⊕ y = y * y * x.
and ☆, the rules are as follows:
when the sum of x and y is even, x ☆ y = y - x + y * x - y;
otherwise, x ☆ y = 3 * (x - 4) + y.
and ⊙, the rules are as follows:
when x is greater than y, x ⊙ y = x / y * y - x - x;
otherwise, x ⊙ y = x - y / 2 - 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: 10 ☆ 7 ⊙ 8 ⊕ 5
Please fill your final answer in \boxed{}. | {
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"condition": "x和y的和是偶数",
"operation": " y - x + y * x - y"
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],
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"precedence": 1
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"question": "Define ⊕, the rules are as follows:\nwhen x is a multiple of 5, x ⊕ y = x * x + y * y - x;\notherwise, x ⊕ y = y * y * x.\nand ☆, the rules are as follows:\nwhen the sum of x and y is even, x ☆ y = y - x + y * x - y;\notherwise, x ☆ y = 3 * (x - 4) + y.\nand ⊙, the rules are as follows:\nwhen x is greater than y, x ⊙ y = x / y * y - x - x;\notherwise, x ⊙ y = x - y / 2 - 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: 10 ☆ 7 ⊙ 8 ⊕ 5\nPlease fill your final answer in \\boxed{}."
},
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logic-v2 | Define ☆, the rules are as follows:
on the real number field, x ☆ y = y - y + y - x + abs(y).
and ▽, the rules are as follows:
on the real number field, x ▽ y = x + 3 - y / 5 - 3.
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 ☆ 5 ▽ 5
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 = y - y + y - x + abs(y).\nand ▽, the rules are as follows:\non the real number field, x ▽ y = x + 3 - y / 5 - 3.\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 ☆ 5 ▽ 5\nPlease fill your final answer in \\boxed{}."
},
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"simplified_expr": "( ((4 ** (( 5 - 5 + 5 - 7 + abs(5))))) + 3 - 5 / 5 - 3)",
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} |
logic-v2 | Define ⊕, the rules are as follows:
on the real number field, x ⊕ y = x - abs(x + y).
and △, the rules are as follows:
on the real number field, x △ y = y / x * y.
and ◇, the rules are as follows:
on the real number field, 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: 3 ⊕ 10 / 3 ◇ 3 △ 5 △ 7
Please fill your final answer in \boxed{}. | {
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"conditions": [],
"default_operation": " x * x + y",
"precedence": 3
},
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
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},
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logic-v2 | 定义 ⊕，规则如下：
当x是奇数时，x ⊕ y = 4 * y * x；
其他情况下，x ⊕ y = y - x * 5。
和 ☆，规则如下：
实数域上，x ☆ y = y + x ⊕ 2。
和 □，规则如下：
实数域上，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: 1 - 4 ⊕ 9 □ 5 ☆ 2
请将最终答案填入\boxed{}中。 | {
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"♢": null
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logic-v2 | 定义 ○，规则如下：
当x是3的倍数时，x ○ y = x - y / x；
其他情况下，x ○ y = x - y + y - 4。
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 ○ 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3的倍数时，x ○ y = x - y / x；\n其他情况下，x ○ y = x - y + y - 4。\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 ○ 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 = y / (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: 7
请将最终答案填入\boxed{}中。 | {
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"answer": "7",
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"question": "定义 △，规则如下：\n实数域上，x △ y = y / (1 / 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: 7\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和y都是偶数时，x ☆ y = abs(x * y)；
其他情况下，x ☆ y = (x) * y + 5。
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: 3 ☆ 3 ◇ 3 - 6
请将最终答案填入\boxed{}中。 | {
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"answer": "55",
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"question": "定义 ☆，规则如下：\n当x和y都是偶数时，x ☆ y = abs(x * y)；\n其他情况下，x ☆ y = (x) * y + 5。\n和 ◇，规则如下：\n实数域上，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: 3 ☆ 3 ◇ 3 - 6\n请将最终答案填入\\boxed{}中。"
},
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"seed": 34928987,
"simplified_expr": "(((((( (((((3 * 3)) + 5))) * 3 + 5)) + ((((3 * 3)) + 5))))) - 6)",
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},
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"conditions": [
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"condition": "x和y都是偶数",
"operation": " abs(x * y)"
}
],
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"precedence": 5
},
"♡": null,
"♢": null
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},
"seed": 34928987,
"task_id": 234928987,
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} |
logic-v2 | Define ▽, the rules are as follows:
when the sum of x and y is even, x ▽ y = x - x * x - x - y;
otherwise, x ▽ y = x + x + x / 4 - 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: 8 - 10 ** 8 ▽ 4
Please fill your final answer in \boxed{}. | {
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"answer": "8",
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"target": null,
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"trace_id": "efc736c2-b11c-42d4-9a8c-93b94f3151d0"
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"question": "Define ▽, the rules are as follows:\nwhen the sum of x and y is even, x ▽ y = x - x * x - x - y;\notherwise, x ▽ y = x + x + x / 4 - 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: 8 - 10 ** 8 ▽ 4\nPlease fill your final answer in \\boxed{}."
},
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"simplified_expr": "(8 - ((10 ** (( 8 - 8 * 8 - 8 - 4)))))",
"solutions_count": null,
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"□": null,
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"▽": {
"associativity": "left",
"conditions": [
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"operation": " x - x * x - x - y"
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"default_operation": " x + x + x / 4 - y",
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},
"◇": null,
"○": null,
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"♡": null,
"♢": null
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"seed": 96515789,
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} |
logic-v2 | Define ▽, the rules are as follows:
when the sum of x and y is even, x ▽ y = x + y;
otherwise, x ▽ y = 5 - 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
Please fill your final answer in \boxed{}. | {
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"answer": "6",
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"gpt_response": "",
"metadata": {
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"expression": "6",
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"♢": null
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"target": null,
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"trace_id": "032e67e6-4880-4732-8418-943b138fc49f"
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"question": "Define ▽, the rules are as follows:\nwhen the sum of x and y is even, x ▽ y = x + y;\notherwise, x ▽ y = 5 - 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: 6\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
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"▽": {
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"conditions": [
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"operation": " x + y"
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"default_operation": " 5 - y - x",
"precedence": 3
},
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
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"trace_id": "032e67e6-4880-4732-8418-943b138fc49f"
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logic-v2 | 定义 △，规则如下：
实数域上，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: 9 △ 5 * 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 = 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: 9 △ 5 * 10\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
"closing_sequence": null,
"expression": "9 △ 5 * 10",
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"○": null,
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"♢": null
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"seed": 63266016,
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} |
logic-v2 | Define ▽, the rules are as follows:
on the real number field, x ▽ y = x * y - 2 / 3.
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 % 6 ▽ 7
Please fill your final answer in \boxed{}. | {
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},
"metadata": {
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"expression": "4 % 6 ▽ 7",
"fill_length": null,
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"⊙": null,
"□": null,
"△": null,
"▽": {
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"conditions": [],
"default_operation": " x * y - 2 / 3",
"precedence": 3
},
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
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},
"seed": 61815853,
"task_id": 261815853,
"task_type": "operation"
} |
logic-v2 | Define ♢, the rules are as follows:
on the real number field, x ♢ y = abs(y ** y + x) + y + x.
and □, the rules are as follows:
on the real number field, x □ y = y * 1 + y * x.
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: 1 □ 10 ⊙ 5 ♢ 3 / 5
Please fill your final answer in \boxed{}. | {
"game_data": {
"answer": "816",
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"gpt_response": "",
"metadata": {
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"expression": "1 □ 10 ⊙ 5 ♢ 3 / 5",
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"simplified_expr": "((( abs(3 ** 3 + (((5 + (( ((((10 * 1)) + ((10 * 1)))) * 1 + ((((10 * 1)) + ((10 * 1)))) * ((5 * ((((10 * 1)) + ((10 * 1)))))))))))) + 3 + (((5 + (( ((((10 * 1)) + ((10 * 1)))) * 1 + ((((10 * 1)) + ((10 * 1)))) * ((5 * ((((10 * 1)) + ((10 * 1))))))))))))) / 5)",
"solutions_count": null,
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"precedence": 4
},
"□": {
"associativity": "left",
"conditions": [],
"default_operation": " y * 1 + y * x",
"precedence": 5
},
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": {
"associativity": "left",
"conditions": [],
"default_operation": " abs(y ** y + x) + y + x",
"precedence": 4
}
},
"target": null,
"total_length": null,
"trace_id": "d853fb32-481e-40b5-b249-4b2aa869d68d"
},
"question": "Define ♢, the rules are as follows:\non the real number field, x ♢ y = abs(y ** y + x) + y + x.\nand □, the rules are as follows:\non the real number field, x □ y = y * 1 + y * x.\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: 1 □ 10 ⊙ 5 ♢ 3 / 5\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
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"seed": 51296211,
"simplified_expr": "((( abs(3 ** 3 + (((5 + (( ((((10 * 1)) + ((10 * 1)))) * 1 + ((((10 * 1)) + ((10 * 1)))) * ((5 * ((((10 * 1)) + ((10 * 1)))))))))))) + 3 + (((5 + (( ((((10 * 1)) + ((10 * 1)))) * 1 + ((((10 * 1)) + ((10 * 1)))) * ((5 * ((((10 * 1)) + ((10 * 1))))))))))))) / 5)",
"solutions_count": null,
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},
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"precedence": 5
},
"△": null,
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"conditions": [],
"default_operation": " abs(y ** y + x) + y + x",
"precedence": 4
}
},
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},
"seed": 51296211,
"task_id": 251296211,
"task_type": "operation"
} |
logic-v2 | Define ◇, the rules are as follows:
when x is a multiple of 3, x ◇ y = y * x * 2 - y;
otherwise, x ◇ 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: 6 ◇ 5
Please fill your final answer in \boxed{}. | {
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"solutions_count": null,
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"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
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"target": null,
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"trace_id": "b700acd6-d8c7-4a23-b7c8-b6963040804a"
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"question": "Define ◇, the rules are as follows:\nwhen x is a multiple of 3, x ◇ y = y * x * 2 - y;\notherwise, x ◇ y = 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: 6 ◇ 5\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
"closing_sequence": null,
"expression": "6 ◇ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
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"seed": 37349919,
"simplified_expr": "( 5 * 6 * 2 - 5)",
"solutions_count": null,
"symbol_definitions": {
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"⊗": null,
"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": {
"associativity": "left",
"conditions": [
{
"condition": "x是3的倍数",
"operation": " y * x * 2 - y"
}
],
"default_operation": " y * y + x",
"precedence": 5
},
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
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"seed": 37349919,
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logic-v2 | Define ♢, the rules are as follows:
when x is odd, x ♢ y = (y) ** y ** x;
otherwise, x ♢ y = y * x * y.
and ☆, the rules are as follows:
on the real number field, x ☆ y = x + y * x.
and ▽, the rules are as follows:
when x is even, x ▽ y = x - 4 * y;
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: 2 ♢ 7 ▽ 5 - 6 ☆ 3
Please fill your final answer in \boxed{}. | {
"game_data": {
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"expression": "2 ♢ 7 ▽ 5 - 6 ☆ 3",
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"▽": {
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"default_operation": " abs(x / x * y)",
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"◇": null,
"○": null,
"◎": null,
"☆": {
"associativity": "left",
"conditions": [],
"default_operation": " x + y * x",
"precedence": 2
},
"♡": null,
"♢": {
"associativity": "left",
"conditions": [
{
"condition": "x是奇数",
"operation": " (y) ** y ** x"
}
],
"default_operation": " y * x * y",
"precedence": 2
}
},
"target": null,
"total_length": null,
"trace_id": "68f5700a-ca80-43dc-b63d-07ea5443300f"
},
"question": "Define ♢, the rules are as follows:\nwhen x is odd, x ♢ y = (y) ** y ** x;\notherwise, x ♢ y = y * x * y.\nand ☆, the rules are as follows:\non the real number field, x ☆ y = x + y * x.\nand ▽, the rules are as follows:\nwhen x is even, x ▽ y = x - 4 * y;\notherwise, x ▽ y = abs(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: 2 ♢ 7 ▽ 5 - 6 ☆ 3\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
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"expression": "2 ♢ 7 ▽ 5 - 6 ☆ 3",
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"seed": 71601104,
"simplified_expr": "((( (( 7 * 2 * 7)) - 4 * 5)) - (( 6 + 3 * 6)))",
"solutions_count": null,
"symbol_definitions": {
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"⊗": null,
"⊙": null,
"□": null,
"△": null,
"▽": {
"associativity": "left",
"conditions": [
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"condition": "x是偶数",
"operation": " x - 4 * y"
}
],
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"precedence": 2
},
"◇": null,
"○": null,
"◎": null,
"☆": {
"associativity": "left",
"conditions": [],
"default_operation": " x + y * x",
"precedence": 2
},
"♡": null,
"♢": {
"associativity": "left",
"conditions": [
{
"condition": "x是奇数",
"operation": " (y) ** y ** x"
}
],
"default_operation": " y * x * y",
"precedence": 2
}
},
"target": null,
"total_length": null,
"trace_id": "68f5700a-ca80-43dc-b63d-07ea5443300f"
},
"seed": 71601104,
"task_id": 271601104,
"task_type": "operation"
} |
logic-v2 | 定义 ○，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: 6 ○ 10 ○ 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 = 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 ○ 10 ○ 2\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
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"expression": "6 ○ 10 ○ 2",
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"□": null,
"△": null,
"▽": null,
"◇": null,
"○": {
"associativity": "left",
"conditions": [],
"default_operation": " y + y - x",
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"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
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"trace_id": "4e5aafe5-087d-4430-bae5-ae2d56d8f787"
},
"seed": 11880363,
"task_id": 211880363,
"task_type": "operation"
} |
logic-v2 | 定义 ⊙，规则如下：
当y是5的倍数时，x ⊙ y = 3 - y ** abs(x + y)；
其他情况下，x ⊙ y = (x + x - y)。
和 ○，规则如下：
实数域上，x ○ y = y + y * x - y。
和 ☆，规则如下：
实数域上，x ☆ 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: 2 ☆ 7 ⊙ 7 * 7 ○ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "2401",
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"gpt_response": "",
"metadata": {
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"expression": "2 ☆ 7 ⊙ 7 * 7 ○ 7",
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"conditions": [],
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},
"◎": null,
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"associativity": "left",
"conditions": [],
"default_operation": " (y * x + y ○ x)",
"precedence": 5
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"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "2e4250a6-0851-45a3-89a8-0ffe80411798"
},
"question": "定义 ⊙，规则如下：\n当y是5的倍数时，x ⊙ y = 3 - y ** abs(x + y)；\n其他情况下，x ⊙ y = (x + x - y)。\n和 ○，规则如下：\n实数域上，x ○ y = y + y * x - y。\n和 ☆，规则如下：\n实数域上，x ☆ 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: 2 ☆ 7 ⊙ 7 * 7 ○ 7\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
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"simplified_expr": "((( ((((((7 * 2)) + (( 2 + 2 * 7 - 2))))) + (((((7 * 2)) + (( 2 + 2 * 7 - 2))))) - 7))) * (( 7 + 7 * 7 - 7)))",
"solutions_count": null,
"symbol_definitions": {
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"conditions": [
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"condition": "y是5的倍数",
"operation": " 3 - y ** abs(x + y)"
}
],
"default_operation": " (x + x - y)",
"precedence": 3
},
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": {
"associativity": "left",
"conditions": [],
"default_operation": " y + y * x - y",
"precedence": 5
},
"◎": null,
"☆": {
"associativity": "left",
"conditions": [],
"default_operation": " (y * x + y ○ x)",
"precedence": 5
},
"♡": null,
"♢": null
},
"target": null,
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},
"seed": 47476819,
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"task_type": "operation"
} |
logic-v2 | Define □, the rules are as follows:
on the real number field, x □ y = x + y / y.
and ♢, the rules are as follows:
when the sum of x and y is odd, x ♢ y = y * y + y * x;
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: 9 ♢ 2 □ 7 □ 8
Please fill your final answer in \boxed{}. | {
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"symbol_definitions": {
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"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": {
"associativity": "left",
"conditions": [
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"condition": "x和y的和是奇数",
"operation": " y * y + y * x"
}
],
"default_operation": " x - (y - y)",
"precedence": 4
}
},
"target": null,
"total_length": null,
"trace_id": "e3c18ac4-62a4-4698-ae2d-e4c9fec41020"
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"question": "Define □, the rules are as follows:\non the real number field, x □ y = x + y / y.\nand ♢, the rules are as follows:\nwhen the sum of x and y is odd, x ♢ y = y * y + y * x;\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: 9 ♢ 2 □ 7 □ 8\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
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"expression": "9 ♢ 2 □ 7 □ 8",
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"n_types": null,
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"seed": 29392642,
"simplified_expr": "( (( (( 2 * 2 + 2 * 9)) + 7 / 7)) + 8 / 8)",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": {
"associativity": "left",
"conditions": [],
"default_operation": " x + y / y",
"precedence": 3
},
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": {
"associativity": "left",
"conditions": [
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"condition": "x和y的和是奇数",
"operation": " y * y + y * x"
}
],
"default_operation": " x - (y - y)",
"precedence": 4
}
},
"target": null,
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"trace_id": "e3c18ac4-62a4-4698-ae2d-e4c9fec41020"
},
"seed": 29392642,
"task_id": 229392642,
"task_type": "operation"
} |
logic-v2 | 定义 △，规则如下：
当x和y都是偶数时，x △ y = 2 * 1 + y - x - x；
其他情况下，x △ y = x + 2 ** 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: 6 △ 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和y都是偶数时，x △ y = 2 * 1 + y - x - x；\n其他情况下，x △ y = x + 2 ** y * x + 3。\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 △ 2 % 3\n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 even, x ○ y = x / x * y + y;
otherwise, x ○ y = abs(4 * 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: 8
Please fill your final answer in \boxed{}. | {
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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y是3的倍数时，x ▽ y = x ♢ x - x * y * x；
其他情况下，x ▽ y = y ** abs(x * x) + x。
和 □，规则如下：
实数域上，x □ y = 3 + x - 5 * 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: 7 □ 10 ▽ 1 ♢ 7 ▽ 3
请将最终答案填入\boxed{}中。 | {
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},
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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y是3的倍数时，x ▽ y = x ♢ x - x * y * x；\n其他情况下，x ▽ y = y ** abs(x * x) + x。\n和 □，规则如下：\n实数域上，x □ y = 3 + x - 5 * 4 + 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: 7 □ 10 ▽ 1 ♢ 7 ▽ 3\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
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"expression": "7 □ 10 ▽ 1 ♢ 7 ▽ 3",
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"seed": 19045825,
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} |
logic-v2 | 定义 ◎，规则如下：
当x和y都是偶数时，x ◎ y = 3 + x + y + 4；
其他情况下，x ◎ y = x * abs(x) - y。
和 ⊗，规则如下：
当x是偶数时，x ⊗ y = (y ◎ 2 - 1 + x)；
其他情况下，x ⊗ y = 1 - x - y * 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: 10 ⊗ 4 ◎ 3
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当x和y都是偶数时，x ◎ y = 3 + x + y + 4；\n其他情况下，x ◎ y = x * abs(x) - y。\n和 ⊗，规则如下：\n当x是偶数时，x ⊗ y = (y ◎ 2 - 1 + x)；\n其他情况下，x ⊗ y = 1 - x - y * 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: 10 ⊗ 4 ◎ 3\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
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logic-v2 | 定义 ◇，规则如下：
当y是3的倍数时，x ◇ y = y + abs(x - y)；
其他情况下，x ◇ 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: 7 ◇ 3 ◇ 5 * 4
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5的倍数时，x ◎ y = y + 1 * x * y；
其他情况下，x ◎ y = x * y - y。
和 ⊗，规则如下：
当y是奇数时，x ⊗ y = x / abs(x + y / y)；
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: 5 ◎ 9 ⊗ 2
请将最终答案填入\boxed{}中。 | {
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"conditions": [
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],
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"seed": 19818830,
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} |
logic-v2 | 定义 ⊗，规则如下：
当x和y都是偶数时，x ⊗ y = 2 + y ** x；
其他情况下，x ⊗ y = y * x / y。
和 ☆，规则如下：
当x是5的倍数时，x ☆ y = y + x + x；
其他情况下，x ☆ y = x + y。
和 ♡，规则如下：
当y是5的倍数时，x ♡ y = y * x ☆ y；
其他情况下，x ♡ y = y ⊗ 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: 7 ☆ 4 ♡ 7 ⊗ 5 ⊗ 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是偶数时，x ♡ y = x / x * y；
其他情况下，x ♡ y = y + x - y。
和 ⊙，规则如下：
实数域上，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: 6 ♡ 8 ⊙ 4
请将最终答案填入\boxed{}中。 | {
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},
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logic-v2 | Define ▽, the rules are as follows:
on the real number field, 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: 4
Please 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 = y - y - 1 - x；
其他情况下，x △ y = x + abs(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: 8
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 * 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: 3 / 4 - 8 △ 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大于y时，x △ 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: 2 △ 2
请将最终答案填入\boxed{}中。 | {
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logic-v2 | 定义 ⊗，规则如下：
当y是偶数时，x ⊗ y = x * 3 - y；
其他情况下，x ⊗ y = y - x - x。
和 ⊕，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) ⊕ 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: 10 ♡ 7 ⊗ 1 ⊕ 3 - 3
请将最终答案填入\boxed{}中。 | {
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],
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},
"♢": null
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"question": "定义 ⊗，规则如下：\n当y是偶数时，x ⊗ y = x * 3 - y；\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 * (x - y)。\n和 ♡，规则如下：\n实数域上，x ♡ y = (y * 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: 10 ♡ 7 ⊗ 1 ⊕ 3 - 3\n请将最终答案填入\\boxed{}中。"
},
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"simplified_expr": "((( 3 * ((( 1 - ((( 7 * (((7 * 10)) - 7)))) - ((( 7 * (((7 * 10)) - 7)))))) - 3))) - 3)",
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"♢": null
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"seed": 40672643,
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logic-v2 | Define ○, the rules are as follows:
when x is less than y, x ○ y = 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: 7 / 2 ○ 10
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 + x * x。
和 △，规则如下：
实数域上，x △ y = (4 ** x + y + x)。
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 = 4 + 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 △ 8
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 - y + x * x。\n和 △，规则如下：\n实数域上，x △ y = (4 ** x + y + x)。\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 = 4 + 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 △ 8\n请将最终答案填入\\boxed{}中。"
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},
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"○": null,
"◎": null,
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"♢": {
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"default_operation": " y * x - y + x * x",
"precedence": 5
}
},
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} |
logic-v2 | Define ♢, the rules are as follows:
on the real number field, x ♢ y = abs(2 ** 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 ♢ 7
Please fill your final answer in \boxed{}. | {
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},
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"seed": 64470220,
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"task_type": "operation"
} |
logic-v2 | Define ◎, the rules are as follows:
on the real number field, x ◎ y = y + x * y * 1 - x.
and △, the rules are as follows:
on the real number field, x △ y = x ◎ 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: 2 + 7 - 8 △ 3 ◎ 5
Please fill your final answer in \boxed{}. | {
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"simplified_expr": "(((2 + 7)) - ((((((( ((((5 + ((((3 * 5)) * 1)))) - 3)) + 8 * ((((5 + ((((3 * 5)) * 1)))) - 3)) * 1 - 8)) - 8)) + 8))))",
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"question": "Define ◎, the rules are as follows:\non the real number field, x ◎ y = y + x * y * 1 - x.\nand △, the rules are as follows:\non the real number field, x △ y = x ◎ 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: 2 + 7 - 8 △ 3 ◎ 5\nPlease fill your final answer in \\boxed{}."
},
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"seed": 63480034,
"simplified_expr": "(((2 + 7)) - ((((((( ((((5 + ((((3 * 5)) * 1)))) - 3)) + 8 * ((((5 + ((((3 * 5)) * 1)))) - 3)) * 1 - 8)) - 8)) + 8))))",
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"♢": null
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},
"seed": 63480034,
"task_id": 263480034,
"task_type": "operation"
} |
logic-v2 | Define △, the rules are as follows:
on the real number field, 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 * 10 △ 8 % 3
Please fill your final answer in \boxed{}. | {
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logic-v2 | Define ⊗, the rules are as follows:
when y is even, x ⊗ y = 2 + x - y - y ** 3;
otherwise, x ⊗ y = x - x * y + x + x.
and ◎, the rules are as follows:
when y is a multiple of 3, x ◎ y = x ** y * x - x + 5;
otherwise, x ◎ y = y + 3 ⊗ x + x.
and ♢, the rules are as follows:
on the real number field, x ♢ y = abs(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: 5 ◎ 4 ⊗ 10 ♢ 3 % 3
Please fill your final answer in \boxed{}. | {
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"question": "Define ⊗, the rules are as follows:\nwhen y is even, x ⊗ y = 2 + x - y - y ** 3;\notherwise, x ⊗ y = x - x * y + x + x.\nand ◎, the rules are as follows:\nwhen y is a multiple of 3, x ◎ y = x ** y * x - x + 5;\notherwise, x ◎ y = y + 3 ⊗ x + x.\nand ♢, the rules are as follows:\non the real number field, x ♢ y = abs(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: 5 ◎ 4 ⊗ 10 ♢ 3 % 3\nPlease fill your final answer in \\boxed{}."
},
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"simplified_expr": "((( (((((4 + (( 3 - 3 * 5 + 3 + 3)))) + 5))) - (((((4 + (( 3 - 3 * 5 + 3 + 3)))) + 5))) * (( abs(3 * 10 + 3) + 10)) + (((((4 + (( 3 - 3 * 5 + 3 + 3)))) + 5))) + (((((4 + (( 3 - 3 * 5 + 3 + 3)))) + 5))))) % 3)",
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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:
on the real number field, x ▽ y = (y - y) + x + 3.
and □, the rules are as follows:
when x is equal to y, x □ y = y ♢ y / x;
otherwise, x □ 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 ▽ 7 ♢ 7 □ 2
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 = (y) + x.\nand ▽, the rules are as follows:\non the real number field, x ▽ y = (y - y) + x + 3.\nand □, the rules are as follows:\nwhen x is equal to y, x □ y = y ♢ y / x;\notherwise, x □ y = (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: 7 ▽ 7 ♢ 7 □ 2\nPlease 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 ** 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: 6
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 = x * y ** x + 1.
and ◇, the rules are as follows:
on the real number field, x ◇ y = 1 - x * y.
and △, the rules are as follows:
when the sum of x and y is even, x △ y = 4 / y - x * 3;
otherwise, x △ y = y + y + x + 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: 8 △ 6 ◇ 10
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 = x * y ** x + 1.\nand ◇, the rules are as follows:\non the real number field, x ◇ y = 1 - x * y.\nand △, the rules are as follows:\nwhen the sum of x and y is even, x △ y = 4 / y - x * 3;\notherwise, x △ y = y + y + x + 2.\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: 8 △ 6 ◇ 10\nPlease 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y是偶数时，x ◇ y = y * abs(y + x)；
其他情况下，x ◇ y = x + y - x。
和 △，规则如下：
当x大于y时，x △ y = y + x；
其他情况下，x △ y = abs(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 △ 3 ◇ 6 ⊙ 3
请将最终答案填入\boxed{}中。 | {
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},
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logic-v2 | Define ⊙, the rules are as follows:
when y is odd, x ⊙ y = y / (x) * x;
otherwise, x ⊙ y = x * (y).
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 = 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: 10 ⊙ 1 □ 6 △ 4 - 1
Please fill your final answer in \boxed{}. | {
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"♢": null
},
"target": null,
"total_length": null,
"trace_id": "f1e317b9-284f-41be-8af6-c79ec928a91f"
},
"seed": 33682655,
"task_id": 233682655,
"task_type": "operation"
} |
logic-v2 | 定义 ♡，规则如下：
当y是5的倍数时，x ♡ y = (x / y * x + x)；
其他情况下，x ♡ y = x * (y ** x)。
和 △，规则如下：
实数域上，x △ y = 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: 9 △ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-77",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 △ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null,
"num_of_numbers": null,
"num_symbols": 2,
"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 93718574,
"simplified_expr": "( 9 - 9 * 9 + 4 - 9)",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": {
"associativity": "left",
"conditions": [],
"default_operation": " x - x * x + y - x",
"precedence": 3
},
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": {
"associativity": "left",
"conditions": [
{
"condition": "y是5的倍数",
"operation": " (x / y * x + x)"
}
],
"default_operation": " x * (y ** x)",
"precedence": 5
},
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "076b9771-492e-47e9-8c1f-582d89de8b8b"
},
"question": "定义 ♡，规则如下：\n当y是5的倍数时，x ♡ y = (x / y * x + x)；\n其他情况下，x ♡ y = x * (y ** x)。\n和 △，规则如下：\n实数域上，x △ y = 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: 9 △ 4\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
"closing_sequence": null,
"expression": "9 △ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null,
"num_of_numbers": null,
"num_symbols": 2,
"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 93718574,
"simplified_expr": "( 9 - 9 * 9 + 4 - 9)",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": {
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"conditions": [],
"default_operation": " x - x * x + y - x",
"precedence": 3
},
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": {
"associativity": "left",
"conditions": [
{
"condition": "y是5的倍数",
"operation": " (x / y * x + x)"
}
],
"default_operation": " x * (y ** x)",
"precedence": 5
},
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "076b9771-492e-47e9-8c1f-582d89de8b8b"
},
"seed": 93718574,
"task_id": 293718574,
"task_type": "operation"
} |
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