env stringclasses 1
value | prompt stringlengths 119 673 | extra dict |
|---|---|---|
logic-v2 | 定义 ♡，规则如下：
实数域上，x ♡ y = x ** 2 / 5 + y + 5。
和 ⊙，规则如下：
实数域上，x ⊙ y = y + y ♡ x * 1。
运算优先级：♡ = ⊙ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 ⊙ 5 ♡ 4 * 2
请将最终答案填入\boxed{}中。 | {
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"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": {
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"default_operation": " x ** 2 / 5 + y + 5",
"precedence": 4
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"♢": null
},
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"question": "定义 ♡，规则如下：\n实数域上，x ♡ y = x ** 2 / 5 + y + 5。\n和 ⊙，规则如下：\n实数域上，x ⊙ y = y + y ♡ x * 1。\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 ⊙ 5 ♡ 4 * 2\n请将最终答案填入\\boxed{}中。"
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"expression": "2 ⊙ 5 ♡ 4 * 2",
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"num_of_numbers": null,
"num_symbols": 2,
"numbers": null,
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"question_sequence": null,
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"simplified_expr": "((( (((5 + (((( 5 ** 2 / 5 + 2 + 5)) * 1))))) ** 2 / 5 + 4 + 5)) * 2)",
"solutions_count": null,
"symbol_definitions": {
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"⊙": {
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"default_operation": " y + y ♡ x * 1",
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"□": null,
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": {
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"conditions": [],
"default_operation": " x ** 2 / 5 + y + 5",
"precedence": 4
},
"♢": null
},
"target": null,
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"seed": 80373848,
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logic-v2 | 定义 ⊗，规则如下：
实数域上，x ⊗ y = y / x。
和 ◇，规则如下：
当x小于y时，x ◇ y = x - y + x；
其他情况下，x ◇ y = (x) ⊗ y。
和 ☆，规则如下：
实数域上，x ☆ y = (y ◇ 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 ⊗ 10 ◇ 4 ☆ 8
请将最终答案填入\boxed{}中。 | {
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"conditions": [],
"default_operation": " (y ◇ x / y)",
"precedence": 5
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"♡": null,
"♢": null
},
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"question": "定义 ⊗，规则如下：\n实数域上，x ⊗ y = y / x。\n和 ◇，规则如下：\n当x小于y时，x ◇ y = x - y + x；\n其他情况下，x ◇ y = (x) ⊗ y。\n和 ☆，规则如下：\n实数域上，x ☆ y = (y ◇ 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: 6 ⊗ 10 ◇ 4 ☆ 8\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
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"expression": "6 ⊗ 10 ◇ 4 ☆ 8",
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"simplified_expr": "(( ((((4 / 8)) / 8)) / ((10 / 6))))",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": {
"associativity": "left",
"conditions": [],
"default_operation": " y / x",
"precedence": 3
},
"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": {
"associativity": "left",
"conditions": [
{
"condition": "x小于y",
"operation": " x - y + x"
}
],
"default_operation": " (x) ⊗ y",
"precedence": 3
},
"○": null,
"◎": null,
"☆": {
"associativity": "left",
"conditions": [],
"default_operation": " (y ◇ x / y)",
"precedence": 5
},
"♡": null,
"♢": null
},
"target": null,
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"trace_id": "4c578f1c-791f-42d1-afda-ec4866a0a85b"
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logic-v2 | 定义 ◇，规则如下：
实数域上，x ◇ y = y + x * 3 * x。
运算优先级：** = ◇ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 ◇ 1 ** 3
请将最终答案填入\boxed{}中。 | {
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"numbers": null,
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"seed": 15499291,
"simplified_expr": "((( 1 + 2 * 3 * 2)) ** 3)",
"solutions_count": null,
"symbol_definitions": {
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},
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"simplified_expr": "((( 1 + 2 * 3 * 2)) ** 3)",
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"♡": null,
"♢": null
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logic-v2 | 定义 ○，规则如下：
实数域上，x ○ y = y / 5 ** x。
和 □，规则如下：
实数域上，x □ y = y * x - 1 * 2。
和 ⊙，规则如下：
当x和y的和是偶数时，x ⊙ y = x * y + x + y；
其他情况下，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 ⊙ 10 □ 1
请将最终答案填入\boxed{}中。 | {
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"simplified_expr": "( 10 * (( 1 * 10 - 1 * 2)) + 10 + (( 1 * 10 - 1 * 2)))",
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"default_operation": " y * x - 1 * 2",
"precedence": 5
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"△": null,
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"○": {
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"default_operation": " y / 5 ** x",
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"simplified_expr": "( 10 * (( 1 * 10 - 1 * 2)) + 10 + (( 1 * 10 - 1 * 2)))",
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"default_operation": " y / x * x",
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"□": {
"associativity": "left",
"conditions": [],
"default_operation": " y * x - 1 * 2",
"precedence": 5
},
"△": null,
"▽": null,
"◇": null,
"○": {
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"default_operation": " y / 5 ** x",
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},
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"♢": null
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logic-v2 | 定义 ♡，规则如下：
当y是3的倍数时，x ♡ y = y / x + 2 + 1 + x；
其他情况下，x ♡ y = abs(3 ** x + x) - y + 2。
和 ♢，规则如下：
当x大于y时，x ♢ y = x - x ♡ y * x / y；
其他情况下，x ♢ y = 4 * y - x ♡ x - 1。
运算优先级：♡ > ** > * = / = % > + = - = ♢。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 ♡ 7
请将最终答案填入\boxed{}中。 | {
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"♢": {
"associativity": "left",
"conditions": [
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"condition": "x大于y",
"operation": " x - x ♡ y * x / y"
}
],
"default_operation": " 4 * y - x ♡ x - 1",
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"expression": "4 ♡ 7",
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"♡": {
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"conditions": [
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"operation": " y / x + 2 + 1 + x"
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],
"default_operation": " abs(3 ** x + x) - y + 2",
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"♢": {
"associativity": "left",
"conditions": [
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"condition": "x大于y",
"operation": " x - x ♡ y * x / y"
}
],
"default_operation": " 4 * y - x ♡ x - 1",
"precedence": 1
}
},
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logic-v2 | 定义 △，规则如下：
当x等于y时，x △ y = abs(y - x - 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: 5 △ 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 + 1 * y.
and ◇, the rules are as follows:
when the sum of x and y is odd, x ◇ y = y + x + 5;
otherwise, x ◇ y = (x ⊙ 3) + y.
and ☆, the rules are as follows:
when x is less than y, x ☆ y = abs(y + x) - 1;
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: 9 ⊙ 2 ◇ 9 ☆ 4
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 + 1 * y.\nand ◇, the rules are as follows:\nwhen the sum of x and y is odd, x ◇ y = y + x + 5;\notherwise, x ◇ y = (x ⊙ 3) + y.\nand ☆, the rules are as follows:\nwhen x is less than y, x ☆ y = abs(y + x) - 1;\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: 9 ⊙ 2 ◇ 9 ☆ 4\nPlease fill your final answer in \\boxed{}."
},
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"operation": " y + x + 5"
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],
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"precedence": 4
},
"○": null,
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"operation": " abs(y + x) - 1"
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],
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"seed": 45014299,
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logic-v2 | Define ⊕, the rules are as follows:
when x is a multiple of 5, x ⊕ y = x * y * x + x + y;
otherwise, x ⊕ y = x * y + abs(x + 4).
and ♡, the rules are as follows:
on the real number field, x ♡ y = x ⊕ y / 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: 4 ▽ 10 ♡ 10 ▽ 8 ⊕ 8
Please fill your final answer in \boxed{}. | {
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"⊗": null,
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"associativity": "left",
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"default_operation": " x - x - y",
"precedence": 5
},
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": {
"associativity": "left",
"conditions": [],
"default_operation": " x ⊕ y / y",
"precedence": 2
},
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "0ef36315-1476-4c32-8641-ffcc67ccf7db"
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"question": "Define ⊕, the rules are as follows:\nwhen x is a multiple of 5, x ⊕ y = x * y * x + x + y;\notherwise, x ⊕ y = x * y + abs(x + 4).\nand ♡, the rules are as follows:\non the real number field, x ♡ y = x ⊕ y / y.\nand ▽, the rules are as follows:\non the real number field, x ▽ y = x - x - y.\nThe precedence of operations: ⊕ = ▽ > ** > * = / = % = ♡ > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 4 ▽ 10 ♡ 10 ▽ 8 ⊕ 8\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
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"expression": "4 ▽ 10 ♡ 10 ▽ 8 ⊕ 8",
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"simplified_expr": "(((( ((((4 - 4)) - 10)) * ((((((((10 - 10)) - 8)) * 8)) + (abs((((((10 - 10)) - 8)) + 4))))) + abs(((((4 - 4)) - 10)) + 4))) / ((((((((10 - 10)) - 8)) * 8)) + (abs((((((10 - 10)) - 8)) + 4)))))))",
"solutions_count": null,
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},
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"precedence": 5
},
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"○": null,
"◎": null,
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"conditions": [],
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"seed": 28205010,
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logic-v2 | 定义 ☆，规则如下：
当x小于y时，x ☆ y = y + x - y；
其他情况下，x ☆ y = 4 - y * x。
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: 5 / 10 / 7 ○ 7 ☆ 1
请将最终答案填入\boxed{}中。 | {
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"♢": null
},
"target": null,
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"question": "定义 ☆，规则如下：\n当x小于y时，x ☆ y = y + x - y；\n其他情况下，x ☆ y = 4 - y * x。\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: 5 / 10 / 7 ○ 7 ☆ 1\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
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"seed": 59520109,
"simplified_expr": "( (((((5 / 10)) / 7)) * (( 4 - 1 * 7)) * ((((5 / 10)) / 7))))",
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"conditions": [
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"condition": "x小于y",
"operation": " y + x - y"
}
],
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"precedence": 4
},
"♡": null,
"♢": null
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},
"seed": 59520109,
"task_id": 259520109,
"task_type": "operation"
} |
logic-v2 | Define ♡, the rules are as follows:
on the real number field, x ♡ y = y - x * (y * y).
and ▽, the rules are as follows:
on the real number field, x ▽ y = x * x / y * x.
The precedence of operations: ♡ > ** = ▽ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 4 ▽ 7 ♡ 7
Please fill your final answer in \boxed{}. | {
"game_data": {
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"♢": null
},
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"trace_id": "d0f34fc7-d0eb-4e18-90b6-2f5cfc14c88b"
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"question": "Define ♡, the rules are as follows:\non the real number field, x ♡ y = y - x * (y * y).\nand ▽, the rules are as follows:\non the real number field, x ▽ y = x * x / y * x.\nThe precedence of operations: ♡ > ** = ▽ > * = / = % > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 4 ▽ 7 ♡ 7\nPlease fill your final answer in \\boxed{}."
},
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},
"seed": 52588797,
"task_id": 252588797,
"task_type": "operation"
} |
logic-v2 | 定义 ♡，规则如下：
实数域上，x ♡ y = x + abs(y) + x。
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: 9 ☆ 9 ♡ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "28",
"difficulty": 1,
"gpt_response": "",
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"expression": "9 ☆ 9 ♡ 10",
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"conditions": [],
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"♢": null
},
"target": null,
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"trace_id": "66cd326a-62e3-4eb3-a695-bd0d61238033"
},
"question": "定义 ♡，规则如下：\n实数域上，x ♡ y = x + abs(y) + x。\n和 ☆，规则如下：\n实数域上，x ☆ y = x + y - y。\n运算优先级：** > * = / = % > + = - = ♡ = ☆。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 9 ☆ 9 ♡ 10\n请将最终答案填入\\boxed{}中。"
},
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"expression": "9 ☆ 9 ♡ 10",
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"seed": 86713906,
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"○": null,
"◎": null,
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},
"♡": {
"associativity": "left",
"conditions": [],
"default_operation": " x + abs(y) + x",
"precedence": 1
},
"♢": null
},
"target": null,
"total_length": null,
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},
"seed": 86713906,
"task_id": 286713906,
"task_type": "operation"
} |
logic-v2 | Define ⊙, the rules are as follows:
when y is odd, x ⊙ y = y - x + 5 * y;
otherwise, x ⊙ y = abs(3 * x + y).
and ◇, the rules are as follows:
on the real number field, x ◇ y = x * y * 5.
and ☆, the rules are as follows:
when x is equal to y, x ☆ y = y ** x ** x;
otherwise, x ☆ 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: 5 ⊙ 3 ☆ 7 ◇ 1
Please fill your final answer in \boxed{}. | {
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"expression": "5 ⊙ 3 ☆ 7 ◇ 1",
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"□": null,
"△": null,
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},
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"◎": null,
"☆": {
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"conditions": [
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"operation": " y ** x ** x"
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],
"default_operation": " y + x - x + y",
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},
"♡": null,
"♢": null
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"question": "Define ⊙, the rules are as follows:\nwhen y is odd, x ⊙ y = y - x + 5 * y;\notherwise, x ⊙ y = abs(3 * x + y).\nand ◇, the rules are as follows:\non the real number field, x ◇ y = x * y * 5.\nand ☆, the rules are as follows:\nwhen x is equal to y, x ☆ y = y ** x ** x;\notherwise, x ☆ y = y + x - x + y.\nThe precedence of operations: ☆ > ** > * = / = % = ◇ > + = - = ⊙。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 5 ⊙ 3 ☆ 7 ◇ 1\nPlease fill your final answer in \\boxed{}."
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logic-v2 | Define ⊕, the rules are as follows:
when y is even, x ⊕ y = 3 - x + y - x * y;
otherwise, x ⊕ y = y - y - x.
and ⊙, the rules are as follows:
when x is a multiple of 3, x ⊙ y = y + x + 5 + y;
otherwise, x ⊙ y = x * x - x / y + x.
and ☆, the rules are as follows:
on the real number field, x ☆ y = (y) * 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: 8 ☆ 6 + 8 ⊕ 8 ⊙ 6
Please fill your final answer in \boxed{}. | {
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"question": "Define ⊕, the rules are as follows:\nwhen y is even, x ⊕ y = 3 - x + y - x * y;\notherwise, x ⊕ y = y - y - x.\nand ⊙, the rules are as follows:\nwhen x is a multiple of 3, x ⊙ y = y + x + 5 + y;\notherwise, x ⊙ y = x * x - x / y + x.\nand ☆, the rules are as follows:\non the real number field, x ☆ y = (y) * x - 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: 8 ☆ 6 + 8 ⊕ 8 ⊙ 6\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 = x * y + x - y。
和 ⊗，规则如下：
实数域上，x ⊗ y = 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: 1 ◎ 8 ⊗ 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 = x * y + x - y。\n和 ⊗，规则如下：\n实数域上，x ⊗ y = 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: 1 ◎ 8 ⊗ 8\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 = x - y - y;
otherwise, x ♢ y = y * x - x ** y.
and ◎, the rules are as follows:
when x is even, x ◎ y = x * y - y * y;
otherwise, x ◎ y = (5 * x - 5 + 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: 5 ♢ 4 ◎ 9
Please fill your final answer in \boxed{}. | {
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},
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logic-v2 | Define ◎, the rules are as follows:
when x and y are both odd, x ◎ y = x ** y * 4 * x / x;
otherwise, x ◎ y = y / x + y * 3.
and ◇, the rules are as follows:
when x and y are both even, x ◇ y = x / y ◎ x;
otherwise, x ◇ y = x * x - x + y * x.
The precedence of operations: ◎ > ** > * = / = % > + = - = ◇。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 10 ◇ 6
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大于y时，x △ y = x - abs(y * 3)；
其他情况下，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: 7 △ 3 / 3
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3的倍数时，x ▽ y = y + x + x；
其他情况下，x ▽ y = y - 1 - 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 ▽ 8 ▽ 5
请将最终答案填入\boxed{}中。 | {
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logic-v2 | 定义 △，规则如下：
当x和y都是奇数时，x △ y = y * x * y * y；
其他情况下，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: 2 △ 4
请将最终答案填入\boxed{}中。 | {
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logic-v2 | 定义 ⊕，规则如下：
实数域上，x ⊕ y = x - y + x。
和 ▽，规则如下：
当x是5的倍数时，x ▽ y = x - (y * x)；
其他情况下，x ▽ y = y ⊕ y - x。
和 ○，规则如下：
当x小于y时，x ○ y = y - x - 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: 2 ⊕ 2 ○ 3 ○ 1 ▽ 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 = x - y + x。\n和 ▽，规则如下：\n当x是5的倍数时，x ▽ y = x - (y * x)；\n其他情况下，x ▽ y = y ⊕ y - x。\n和 ○，规则如下：\n当x小于y时，x ○ y = y - x - y；\n其他情况下，x ○ y = x * x - y。\n运算优先级：** > * = / = % = ○ > + = - = ⊕ = ▽。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 2 ⊕ 2 ○ 3 ○ 1 ▽ 8\n请将最终答案填入\\boxed{}中。"
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logic-v2 | Define △, the rules are as follows:
when y is a multiple of 5, x △ y = y ** 4 - x - x + y;
otherwise, x △ y = y - y / y + x.
The precedence of operations: ** > * = / = % = △ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 7 △ 7
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},
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"⊗": null,
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"△": {
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"conditions": [
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"operation": " y ** 4 - x - x + y"
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logic-v2 | Define ▽, the rules are as follows:
when x and y are both odd, x ▽ y = x - y + y * x;
otherwise, x ▽ y = y + x / y - x * (y).
The precedence of operations: ** = ▽ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 7 % 10 ▽ 10 * 1
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 * x - x;
otherwise, x ♢ y = x + (y) + 4.
and ♡, the rules are as follows:
on the real number field, x ♡ y = x + x + y.
and ▽, the rules are as follows:
when y is a multiple of 5, x ▽ y = 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: 4 ♢ 2 ▽ 10 ♢ 3 ♡ 1
Please fill your final answer in \boxed{}. | {
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"☆": null,
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"associativity": "left",
"conditions": [],
"default_operation": " x + x + y",
"precedence": 2
},
"♢": {
"associativity": "left",
"conditions": [
{
"condition": "x是偶数",
"operation": " y * x - x"
}
],
"default_operation": " x + (y) + 4",
"precedence": 4
}
},
"target": null,
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"question": "Define ♢, the rules are as follows:\nwhen x is even, x ♢ y = y * x - x;\notherwise, x ♢ y = x + (y) + 4.\nand ♡, the rules are as follows:\non the real number field, x ♡ y = x + x + y.\nand ▽, the rules are as follows:\nwhen y is a multiple of 5, x ▽ y = 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: 4 ♢ 2 ▽ 10 ♢ 3 ♡ 1\nPlease fill your final answer in \\boxed{}."
},
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"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": {
"associativity": "left",
"conditions": [],
"default_operation": " x + x + y",
"precedence": 2
},
"♢": {
"associativity": "left",
"conditions": [
{
"condition": "x是偶数",
"operation": " y * x - x"
}
],
"default_operation": " x + (y) + 4",
"precedence": 4
}
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logic-v2 | Define ⊗, the rules are as follows:
when y is odd, x ⊗ y = y * x * y + 2;
otherwise, x ⊗ y = x - x / y - x.
and ☆, the rules are as follows:
when y is odd, x ☆ y = y + x + y * y;
otherwise, x ☆ y = x - x * y ⊗ (x).
and ▽, the rules are as follows:
on the real number field, x ▽ y = x + y + x ☆ y.
The precedence of operations: ▽ > ** = ⊗ > * = / = % = ☆ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 5 ☆ 8 ▽ 6
Please fill your final answer in \boxed{}. | {
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"question": "Define ⊗, the rules are as follows:\nwhen y is odd, x ⊗ y = y * x * y + 2;\notherwise, x ⊗ y = x - x / y - x.\nand ☆, the rules are as follows:\nwhen y is odd, x ☆ y = y + x + y * y;\notherwise, x ☆ y = x - x * y ⊗ (x).\nand ▽, the rules are as follows:\non the real number field, x ▽ y = x + y + x ☆ y.\nThe precedence of operations: ▽ > ** = ⊗ > * = / = % = ☆ > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 5 ☆ 8 ▽ 6\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。
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
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 the sum of x and y is odd, x ⊗ y = x + y + y * 4 - 4;
otherwise, x ⊗ y = x + x - y ** y.
and ☆, the rules are as follows:
on the real number field, x ☆ y = x + y - 4 / x.
and ▽, the rules are as follows:
when x and y are both even, x ▽ y = y / y + y * x * x;
otherwise, x ▽ y = (y - x * x) - 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 ⊗ 6 ☆ 10 ▽ 6
Please fill your final answer in \boxed{}. | {
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"question": "Define ⊗, the rules are as follows:\nwhen the sum of x and y is odd, x ⊗ y = x + y + y * 4 - 4;\notherwise, x ⊗ y = x + x - y ** y.\nand ☆, the rules are as follows:\non the real number field, x ☆ y = x + y - 4 / x.\nand ▽, the rules are as follows:\nwhen x and y are both even, x ▽ y = y / y + y * x * x;\notherwise, x ▽ y = (y - x * x) - y ☆ 4.\nThe precedence of operations: ⊗ > ** = ▽ > * = / = % = ☆ > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 5 ⊗ 6 ☆ 10 ▽ 6\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 = x - x + y - 4。
和 ☆，规则如下：
当y是3的倍数时，x ☆ y = 1 / y + y + x；
其他情况下，x ☆ y = y - x - abs(y + x)。
和 ♡，规则如下：
当x和y都是偶数时，x ♡ y = x * y ☆ y + x；
其他情况下，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: 4 ☆ 5 ⊕ 9 ♡ 3
请将最终答案填入\boxed{}中。 | {
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"question": "定义 ⊕，规则如下：\n实数域上，x ⊕ y = x - x + y - 4。\n和 ☆，规则如下：\n当y是3的倍数时，x ☆ y = 1 / y + y + x；\n其他情况下，x ☆ y = y - x - abs(y + x)。\n和 ♡，规则如下：\n当x和y都是偶数时，x ♡ y = x * y ☆ y + x；\n其他情况下，x ♡ y = y - x - x。\n运算优先级：** = ⊕ = ☆ > * = / = % = ♡ > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 4 ☆ 5 ⊕ 9 ♡ 3\n请将最终答案填入\\boxed{}中。"
},
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logic-v2 | 定义 ◎，规则如下：
实数域上，x ◎ y = x + (y)。
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 ◎ 9
请将最终答案填入\boxed{}中。 | {
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logic-v2 | 定义 ◎，规则如下：
当x是3的倍数时，x ◎ y = x ** x * y；
其他情况下，x ◎ y = x + y + (5)。
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: 2 ◎ 4 □ 4
请将最终答案填入\boxed{}中。 | {
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"♢": null
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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 ** x.
and ○, the rules are as follows:
when the sum of x and y is even, x ○ y = 2 ◎ x + y + x;
otherwise, x ○ y = 4 + x * y.
The precedence of operations: ** = ◎ > * = / = % > + = - = ○。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 9 ◎ 6 % 8 ○ 2
Please fill your final answer in \boxed{}. | {
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},
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logic-v2 | Define ⊙, the rules are as follows:
when y is a multiple of 5, x ⊙ y = y + x - 4;
otherwise, x ⊙ y = (y + x) / x.
and □, the rules are as follows:
when x is a multiple of 3, x □ y = y + x ⊙ y;
otherwise, x □ y = y - x ⊙ x.
and ☆, the rules are as follows:
when x is even, 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: 7 ⊙ 10 □ 5
Please fill your final answer in \boxed{}. | {
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"operation": " y ⊙ x * y"
}
],
"default_operation": " (x - x * y)",
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"♡": null,
"♢": null
},
"target": null,
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"question": "Define ⊙, the rules are as follows:\nwhen y is a multiple of 5, x ⊙ y = y + x - 4;\notherwise, x ⊙ y = (y + x) / x.\nand □, the rules are as follows:\nwhen x is a multiple of 3, x □ y = y + x ⊙ y;\notherwise, x □ y = y - x ⊙ x.\nand ☆, the rules are as follows:\nwhen x is even, x ☆ y = y ⊙ x * y;\notherwise, x ☆ y = (x - x * y).\nThe precedence of operations: ☆ > ** = ⊙ = □ > * = / = % > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 7 ⊙ 10 □ 5\nPlease fill your final answer in \\boxed{}."
},
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"○": null,
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"operation": " y ⊙ x * y"
}
],
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},
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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).
The precedence of operations: ▽ > ☆ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 9 % 6 ▽ 5 - 2 ☆ 1
Please fill your final answer in \boxed{}. | {
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},
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"question": "Define ☆, the rules are as follows:\non the real number field, x ☆ y = x + x + y.\nand ▽, the rules are as follows:\non the real number field, x ▽ y = (x ☆ y).\nThe precedence of operations: ▽ > ☆ > ** > * = / = % > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 9 % 6 ▽ 5 - 2 ☆ 1\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 + x / x。
和 ⊕，规则如下：
当y是3的倍数时，x ⊕ y = y - 2 - x ** 4；
其他情况下，x ⊕ y = x + 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: 5 □ 4 □ 2 ⊕ 7
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 - 5 + 4 + y.
and ⊗, the rules are as follows:
when the sum of x and y is odd, x ⊗ y = x + y;
otherwise, x ⊗ y = 5 / (4 * x △ y).
and □, the rules are as follows:
when x is equal to y, x □ y = x / x + y;
otherwise, x □ y = 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: 10 □ 3 ⊗ 10 △ 1
Please fill your final answer in \boxed{}. | {
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},
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},
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
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},
"target": null,
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"question": "Define △, the rules are as follows:\non the real number field, x △ y = x - 5 + 4 + y.\nand ⊗, the rules are as follows:\nwhen the sum of x and y is odd, x ⊗ y = x + y;\notherwise, x ⊗ y = 5 / (4 * x △ y).\nand □, the rules are as follows:\nwhen x is equal to y, x □ y = x / x + y;\notherwise, x □ y = y + y + x + y.\nThe precedence of operations: △ = ⊗ = □ > ** > * = / = % > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 10 □ 3 ⊗ 10 △ 1\nPlease fill your final answer in \\boxed{}."
},
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logic-v2 | 定义 ♢，规则如下：
当y是3的倍数时，x ♢ y = x / x - y；
其他情况下，x ♢ y = x + (y / x - x) * x。
运算优先级：♢ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 * 2 ** 1 ♢ 9
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 / y - x + (y * 2)。
运算优先级：** > * = / = % = ○ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 ○ 8
请将最终答案填入\boxed{}中。 | {
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logic-v2 | Define ♡, the rules are as follows:
when the sum of x and y is even, x ♡ y = x * x - y;
otherwise, x ♡ y = x + y + y.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = x + y.
and ◇, the rules are as follows:
on the real number field, x ◇ y = 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 ⊗ 5 ◇ 10
Please fill your final answer in \boxed{}. | {
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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 = 4 * x / y。
运算优先级：** > * = / = % > + = - = ○。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 ○ 10 / 7 % 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) + y + y.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = x / y + x ♢ y.
and ☆, 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: 6 ⊗ 2 ☆ 7 ♢ 6
Please fill your final answer in \boxed{}. | {
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"precedence": 3
},
"♡": null,
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"conditions": [],
"default_operation": " (x - y) + y + y",
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}
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},
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},
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"conditions": [],
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logic-v2 | Define ♡, the rules are as follows:
on the real number field, x ♡ y = (4 - y * x - y).
and △, the rules are as follows:
on the real number field, x △ y = x + x + y + x.
The precedence of operations: ♡ > △ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 10 ♡ 5
Please fill your final answer in \boxed{}. | {
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"♢": null
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},
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"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": {
"associativity": "left",
"conditions": [],
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"♢": null
},
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logic-v2 | 定义 △，规则如下：
实数域上，x △ y = y * abs(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 % 5 / 3 △ 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和y都是奇数时，x ⊗ y = y - 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。
和 □，规则如下：
当x和y的和是奇数时，x □ y = (x + y) - x；
其他情况下，x □ y = 4 - x - abs(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 ◎ 8 ⊗ 7 □ 2
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logic-v2 | 定义 ◇，规则如下：
当x是3的倍数时，x ◇ y = y - x * x ** x * x；
其他情况下，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 % 8 ◇ 5
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.
The precedence of operations: ▽ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 2 ▽ 6
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 * y - x * x * 5;
otherwise, x ⊙ y = x / 3 * y + y.
and ◎, the rules are as follows:
on the real number field, x ◎ y = 1 / 5 ⊙ x - x * y.
and ○, the rules are as follows:
on the real number field, x ○ y = 1 * 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: 2 ◎ 3 ⊙ 7
Please fill your final answer in \boxed{}. | {
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logic-v2 | 定义 ○，规则如下：
实数域上，x ○ y = y * abs(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: 6 ○ 3 ** 2 - 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 = 4 * y - x - x / y.
and △, the rules are as follows:
on the real number field, x △ 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: 6 △ 8 ☆ 8
Please fill your final answer in \boxed{}. | {
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"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": {
"associativity": "left",
"conditions": [],
"default_operation": " 4 * y - x - x / y",
"precedence": 3
},
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "830cdc00-24cd-4c32-8a14-14285c4ace82"
},
"question": "Define ☆, the rules are as follows:\non the real number field, x ☆ y = 4 * y - x - x / y.\nand △, the rules are as follows:\non the real number field, x △ 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: 6 △ 8 ☆ 8\nPlease fill your final answer in \\boxed{}."
},
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"○": null,
"◎": null,
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},
"seed": 89139953,
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"task_type": "operation"
} |
logic-v2 | 定义 ○，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: 7
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 - y + x；
其他情况下，x ♢ y = (x - y) * y。
和 ○，规则如下：
当x小于y时，x ○ y = abs(x * x) * y；
其他情况下，x ○ y = x - 5 ♢ y。
和 □，规则如下：
当y是奇数时，x □ y = y / x - y；
其他情况下，x □ y = x - y / y。
运算优先级：** = □ > * = / = % = ♢ = ○ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 ♢ 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x和y都是奇数时，x ♢ y = y - y + x；\n其他情况下，x ♢ y = (x - y) * y。\n和 ○，规则如下：\n当x小于y时，x ○ y = abs(x * x) * y；\n其他情况下，x ○ y = x - 5 ♢ y。\n和 □，规则如下：\n当y是奇数时，x □ y = y / x - y；\n其他情况下，x □ y = x - y / y。\n运算优先级：** = □ > * = / = % = ♢ = ○ > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 4 ♢ 9 □ 4\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
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"expression": "4 ♢ 9 □ 4",
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logic-v2 | 定义 ◎，规则如下：
实数域上，x ◎ y = y - x + x。
和 ▽，规则如下：
当x是5的倍数时，x ▽ y = (y ◎ 3) * x；
其他情况下，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: 5 % 1 ◎ 8 ▽ 3
请将最终答案填入\boxed{}中。 | {
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"question": "定义 ◎，规则如下：\n实数域上，x ◎ y = y - x + x。\n和 ▽，规则如下：\n当x是5的倍数时，x ▽ y = (y ◎ 3) * x；\n其他情况下，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: 5 % 1 ◎ 8 ▽ 3\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
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"expression": "5 % 1 ◎ 8 ▽ 3",
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"seed": 33310036,
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} |
logic-v2 | 定义 ◎，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 * abs(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 % 1 ◎ 1 △ 5
请将最终答案填入\boxed{}中。 | {
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},
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"simplified_expr": "( 5 + (( 1 - (1 - ((3 % 1)) - 1))) * abs((( 1 - (1 - ((3 % 1)) - 1))) - (( 1 - (1 - ((3 % 1)) - 1)))))",
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logic-v2 | Define ♡, the rules are as follows:
on the real number field, x ♡ y = y * 2 + y / x - x.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = x ♡ y - 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: 9 ⊗ 6 ♡ 9
Please fill your final answer in \boxed{}. | {
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"♢": null
},
"target": null,
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"question": "Define ♡, the rules are as follows:\non the real number field, x ♡ y = y * 2 + y / x - x.\nand ⊗, the rules are as follows:\non the real number field, x ⊗ y = x ♡ y - y - 4.\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 ⊗ 6 ♡ 9\nPlease fill your final answer in \\boxed{}."
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"solutions_count": null,
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"♢": null
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},
"seed": 83593294,
"task_id": 283593294,
"task_type": "operation"
} |
logic-v2 | 定义 □，规则如下：
实数域上，x □ y = abs(y - x) - x。
和 ♡，规则如下：
当x小于y时，x ♡ y = x / (x) * 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: 10 □ 6 ♡ 5
请将最终答案填入\boxed{}中。 | {
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"operation": " x / (x) * y"
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"♢": null
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"question": "定义 □，规则如下：\n实数域上，x □ y = abs(y - x) - x。\n和 ♡，规则如下：\n当x小于y时，x ♡ y = x / (x) * y；\n其他情况下，x ♡ y = x □ x ** y。\n运算优先级：♡ > ** > * = / = % = □ > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 10 □ 6 ♡ 5\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 odd, x ◎ y = 2 - y * 5 - y * x;
otherwise, x ◎ y = x / y - y / x + x.
and ♡, the rules are as follows:
when y is odd, x ♡ y = x * (x + y) * y;
otherwise, x ♡ y = x * y + x + x * 1.
The precedence of operations: ♡ > ** = ◎ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 9 ◎ 1 % 3 ** 1 ♡ 2
Please fill your final answer in \boxed{}. | {
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"seed": 29813937,
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} |
logic-v2 | Define ◇, 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: 8 ◇ 3 + 3 % 5
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 - 2 + 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: 10 % 5 + 2 ◇ 8
请将最终答案填入\boxed{}中。 | {
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logic-v2 | 定义 □，规则如下：
实数域上，x □ y = (y) / x / x ** y。
和 △，规则如下：
实数域上，x △ y = y + x + 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: 6 △ 8 □ 9
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).
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
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 - y / x；
其他情况下，x ⊗ y = x + y + x。
和 ♢，规则如下：
当x小于y时，x ♢ y = 1 ** x * y；
其他情况下，x ♢ y = (y ⊗ x)。
和 ☆，规则如下：
实数域上，x ☆ y = y * x * y。
运算优先级：♢ > ⊗ > ** > * = / = % = ☆ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 % 10 + 6 ♢ 8 ☆ 10 ⊗ 6
请将最终答案填入\boxed{}中。 | {
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},
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"♢": {
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"operation": " 1 ** x * y"
}
],
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}
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logic-v2 | Define ▽, the rules are as follows:
when y is even, x ▽ y = y - x * y;
otherwise, x ▽ y = y - x * x.
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 = (4 - x) □ x - y.
The precedence of operations: ▽ > ** = ⊕ > * = / = % = □ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 9 ⊕ 2 ▽ 2 □ 7 □ 5
Please fill your final answer in \boxed{}. | {
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},
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},
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"□": {
"associativity": "left",
"conditions": [],
"default_operation": " y - x * y",
"precedence": 2
},
"△": null,
"▽": {
"associativity": "left",
"conditions": [
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"condition": "y是偶数",
"operation": " y - x * y"
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"default_operation": " y - x * x",
"precedence": 5
},
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
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"target": null,
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},
"seed": 79156075,
"task_id": 279156075,
"task_type": "operation"
} |
logic-v2 | 定义 ◎，规则如下：
当x大于y时，x ◎ y = 1 + y / y + 4 + x；
其他情况下，x ◎ y = x + abs(x) * y + y。
和 ⊗，规则如下：
实数域上，x ⊗ y = 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: 3 ⊗ 2
请将最终答案填入\boxed{}中。 | {
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"question": "定义 ◎，规则如下：\n当x大于y时，x ◎ y = 1 + y / y + 4 + x；\n其他情况下，x ◎ y = x + abs(x) * y + y。\n和 ⊗，规则如下：\n实数域上，x ⊗ y = 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: 3 ⊗ 2\n请将最终答案填入\\boxed{}中。"
},
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"solutions_count": null,
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"seed": 3046938,
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} |
logic-v2 | 定义 ◎，规则如下：
当x等于y时，x ◎ y = x / y * x；
其他情况下，x ◎ y = (y + y / y * x)。
和 □，规则如下：
当x是奇数时，x □ y = x ◎ y / (y)；
其他情况下，x □ y = 5 - 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 ◎ 2
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 / y * x；\n其他情况下，x ◎ y = (y + y / y * x)。\n和 □，规则如下：\n当x是奇数时，x □ y = x ◎ y / (y)；\n其他情况下，x □ y = 5 - 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: 8 ◎ 2\n请将最终答案填入\\boxed{}中。"
},
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],
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"△": null,
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"◇": null,
"○": null,
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],
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"seed": 76306564,
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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 = (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: 9 ◇ 9 □ 5 ◇ 3
Please fill your final answer in \boxed{}. | {
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},
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
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"trace_id": "edf85e31-c95a-484f-af91-4c2a057ca871"
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"question": "Define □, the rules are as follows:\non the real number field, x □ y = (y * x) * y.\nand ◇, the rules are as follows:\non the real number field, x ◇ y = (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: 9 ◇ 9 □ 5 ◇ 3\nPlease fill your final answer in \\boxed{}."
},
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"simplified_expr": "( (3) - (( ((( (5 * 9) * 5))) - 9 + (( (5 * 9) * 5)) - 9 / 9)) + 3 - (( ((( (5 * 9) * 5))) - 9 + (( (5 * 9) * 5)) - 9 / 9)) / (( ((( (5 * 9) * 5))) - 9 + (( (5 * 9) * 5)) - 9 / 9)))",
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"▽": null,
"◇": {
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"seed": 79434499,
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"task_type": "operation"
} |
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 - x * 4。
和 △，规则如下：
实数域上，x △ y = x * x - (y + y)。
和 ⊙，规则如下：
当y是5的倍数时，x ⊙ y = y * x + x △ y；
其他情况下，x ⊙ y = abs(2 + y - x - y)。
运算优先级：△ > ** = ♢ > * = / = % > + = - = ⊙。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 △ 3 ⊙ 10
请将最终答案填入\boxed{}中。 | {
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"○": null,
"◎": null,
"☆": null,
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"♢": {
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"question": "定义 ♢，规则如下：\n当x大于y时，x ♢ y = y + x；\n其他情况下，x ♢ y = y - x * 4。\n和 △，规则如下：\n实数域上，x △ y = x * x - (y + y)。\n和 ⊙，规则如下：\n当y是5的倍数时，x ⊙ y = y * x + x △ y；\n其他情况下，x ⊙ y = abs(2 + 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: 8 △ 3 ⊙ 10\n请将最终答案填入\\boxed{}中。"
},
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"operation": " y * x + x △ y"
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],
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},
"□": null,
"△": {
"associativity": "left",
"conditions": [],
"default_operation": " x * x - (y + y)",
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"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": {
"associativity": "left",
"conditions": [
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"operation": " y + x"
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],
"default_operation": " y - x * 4",
"precedence": 3
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"seed": 43436342,
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} |
logic-v2 | 定义 ☆，规则如下：
实数域上，x ☆ y = x - x / x - x + y。
和 ⊙，规则如下：
实数域上，x ⊙ y = x ☆ y + y + x + 2。
运算优先级：⊙ > ** > * = / = % = ☆ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 ⊙ 9 ☆ 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 - x + y。\n和 ⊙，规则如下：\n实数域上，x ⊙ y = x ☆ y + y + x + 2。\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 ⊙ 9 ☆ 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的和是奇数时，x ♡ y = x ** y；
其他情况下，x ♡ y = y / x。
和 ○，规则如下：
实数域上，x ○ y = y ♡ x * 1。
运算优先级：○ > ** > * = / = % = ♡ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ○ 10 ♡ 2 % 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 / y) ** x.
and ♢, the rules are as follows:
on the real number field, x ♢ y = (1) * 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: 1 ** 7 ♢ 5 ☆ 1
Please fill your final answer in \boxed{}. | {
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},
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"simplified_expr": "( ((1 ** (((((1 * 7)) + (( 5 * (7 / 7) ** 5))))))) * (1 / 1) ** ((1 ** (((((1 * 7)) + (( 5 * (7 / 7) ** 5))))))))",
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logic-v2 | 定义 ⊕，规则如下：
当x和y都是偶数时，x ⊕ y = 1 - x / y；
其他情况下，x ⊕ y = y ** (x - y)。
和 ♡，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 + x。
和 □，规则如下：
实数域上，x □ y = x - 1 ♡ 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 ⊕ 3 □ 3 ♡ 6 ⊕ 9
请将最终答案填入\boxed{}中。 | {
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logic-v2 | 定义 ○，规则如下：
实数域上，x ○ y = x * y - x - y * x。
运算优先级：** > * = / = % = ○ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4
请将最终答案填入\boxed{}中。 | {
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logic-v2 | Define ☆, the rules are as follows:
when x is less than y, x ☆ y = y + y * x ** 1;
otherwise, x ☆ y = y + x + x - y.
and ○, the rules are as follows:
when y is even, x ○ y = y * x ☆ 3 * x;
otherwise, x ○ y = y + x - y + x.
The precedence of operations: ** = ○ > * = / = % = ☆ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 8 ○ 5
Please fill your final answer in \boxed{}. | {
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"operation": " y + y * x ** 1"
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"default_operation": " y + x + x - y",
"precedence": 2
},
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"♢": null
},
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"condition": "x小于y",
"operation": " y + y * x ** 1"
}
],
"default_operation": " y + x + x - y",
"precedence": 2
},
"♡": null,
"♢": null
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"seed": 56320967,
"task_id": 256320967,
"task_type": "operation"
} |
logic-v2 | Define ♡, the rules are as follows:
on the real number field, x ♡ y = x + (y).
and ▽, the rules are as follows:
on the real number field, x ▽ y = (x + y) + 5.
The precedence of operations: ▽ > ♡ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 2 / 4 ▽ 10 ♡ 5
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是5的倍数时，x ⊗ y = x + y - y；
其他情况下，x ⊗ y = y + x + 1。
和 ⊕，规则如下：
实数域上，x ⊕ y = y ⊗ x * x。
和 ♢，规则如下：
实数域上，x ♢ y = y + x ⊕ 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 ♢ 7 ⊕ 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:
when the sum of x and y is even, x ◇ y = 5 * y + 5 - x;
otherwise, x ◇ y = y / (x) - y ** x.
and ♢, the rules are as follows:
on the real number field, x ♢ y = y - x * (3 - 1).
and △, the rules are as follows:
on the real number field, x △ y = x + y ** x * y.
The precedence of operations: ◇ > ** > * = / = % = △ > + = - = ♢。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 8 ♢ 3 ◇ 7
Please fill your final answer in \boxed{}. | {
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"question": "Define ◇, the rules are as follows:\nwhen the sum of x and y is even, x ◇ y = 5 * y + 5 - x;\notherwise, x ◇ y = y / (x) - y ** x.\nand ♢, the rules are as follows:\non the real number field, x ♢ y = y - x * (3 - 1).\nand △, the rules are as follows:\non the real number field, x △ y = x + y ** x * y.\nThe precedence of operations: ◇ > ** > * = / = % = △ > + = - = ♢。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 8 ♢ 3 ◇ 7\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 = 5 / x * y / x.
and △, the rules are as follows:
on the real number field, x △ y = y ** 3 + 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 % 7 △ 5 * 9 ♡ 1
Please fill your final answer in \boxed{}. | {
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"question": "Define ♡, the rules are as follows:\non the real number field, x ♡ y = 5 / x * y / x.\nand △, the rules are as follows:\non the real number field, x △ y = y ** 3 + 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 % 7 △ 5 * 9 ♡ 1\nPlease fill your final answer in \\boxed{}."
},
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} |
logic-v2 | 定义 ♡，规则如下：
当y是奇数时，x ♡ y = (y + x)；
其他情况下，x ♡ y = (x) / y。
和 ☆，规则如下：
当x大于y时，x ☆ y = 4 ** 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: 8 ☆ 6 ♡ 8 % 2 ** 6
请将最终答案填入\boxed{}中。 | {
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logic-v2 | 定义 ○，规则如下：
当x是奇数时，x ○ y = y - x + x；
其他情况下，x ○ y = abs(x / 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: 4
请将最终答案填入\boxed{}中。 | {
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"question": "定义 ○，规则如下：\n当x是奇数时，x ○ y = y - x + x；\n其他情况下，x ○ y = abs(x / x * 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: 4\n请将最终答案填入\\boxed{}中。"
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logic-v2 | Define △, the rules are as follows:
when y is odd, x △ y = y + 1 + (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: 4 △ 1 - 2 % 7
Please fill your final answer in \boxed{}. | {
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"answer": "4",
"difficulty": 1,
"gpt_response": "",
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"△": {
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"condition": "y是奇数",
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"trace_id": "67a96afe-236c-4b17-b4b8-fc74cfd06d8d"
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"question": "Define △, the rules are as follows:\nwhen y is odd, x △ y = y + 1 + (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: 4 △ 1 - 2 % 7\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
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"seed": 58755661,
"simplified_expr": "((( 1 + 1 + (4))) - ((2 % 7)))",
"solutions_count": null,
"symbol_definitions": {
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"△": {
"associativity": "left",
"conditions": [
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"condition": "y是奇数",
"operation": " y + 1 + (x)"
}
],
"default_operation": " y * y + x",
"precedence": 1
},
"▽": null,
"◇": null,
"○": null,
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},
"seed": 58755661,
"task_id": 258755661,
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} |
logic-v2 | Define ♡, the rules are as follows:
when x is a multiple of 3, x ♡ y = abs(x) / x * 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: 10 ♡ 2 % 9
Please fill your final answer in \boxed{}. | {
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"answer": "7",
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"gpt_response": "",
"metadata": {
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"expression": "10 ♡ 2 % 9",
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"♡": {
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"condition": "x是3的倍数",
"operation": " abs(x) / x * y + x * y"
}
],
"default_operation": " x * x + x - y - y",
"precedence": 3
},
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "6547b859-a608-4720-9fe3-ee74a86c0554"
},
"question": "Define ♡, the rules are as follows:\nwhen x is a multiple of 3, x ♡ y = abs(x) / x * y + x * y;\notherwise, x ♡ y = x * x + 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: 10 ♡ 2 % 9\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
"closing_sequence": null,
"expression": "10 ♡ 2 % 9",
"fill_length": null,
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"operators": null,
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"seed": 54766022,
"simplified_expr": "((( 10 * 10 + 10 - 2 - 2)) % 9)",
"solutions_count": null,
"symbol_definitions": {
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"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": {
"associativity": "left",
"conditions": [
{
"condition": "x是3的倍数",
"operation": " abs(x) / x * y + x * y"
}
],
"default_operation": " x * x + x - y - y",
"precedence": 3
},
"♢": null
},
"target": null,
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"trace_id": "6547b859-a608-4720-9fe3-ee74a86c0554"
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"seed": 54766022,
"task_id": 254766022,
"task_type": "operation"
} |
logic-v2 | 定义 ⊗，规则如下：
当y是5的倍数时，x ⊗ y = x - (y) / y * 3；
其他情况下，x ⊗ y = (y + x - x)。
和 ○，规则如下：
当x和y都是偶数时，x ○ y = x + x * x + y + y；
其他情况下，x ○ y = x + y / y - y * y。
和 □，规则如下：
当x小于y时，x □ y = y + x；
其他情况下，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: 1 ○ 8 ⊗ 1 □ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ○ 8 ⊗ 1 □ 8",
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"seed": 87375282,
"simplified_expr": "( ((( 8 + 1)) + (( 1 + 8 / 8 - 8 * 8)) - (( 1 + 8 / 8 - 8 * 8))))",
"solutions_count": null,
"symbol_definitions": {
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"default_operation": " (y + x - x)",
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},
"⊙": null,
"□": {
"associativity": "left",
"conditions": [
{
"condition": "x小于y",
"operation": " y + x"
}
],
"default_operation": " y ⊗ x - x * y",
"precedence": 5
},
"△": null,
"▽": null,
"◇": null,
"○": {
"associativity": "left",
"conditions": [
{
"condition": "x和y都是偶数",
"operation": " x + x * x + y + y"
}
],
"default_operation": " x + y / y - y * y",
"precedence": 5
},
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "8c46812f-e869-4517-aa86-5e7b741203e2"
},
"question": "定义 ⊗，规则如下：\n当y是5的倍数时，x ⊗ y = x - (y) / y * 3；\n其他情况下，x ⊗ y = (y + x - x)。\n和 ○，规则如下：\n当x和y都是偶数时，x ○ y = x + x * x + y + y；\n其他情况下，x ○ y = x + y / y - y * y。\n和 □，规则如下：\n当x小于y时，x □ y = y + x；\n其他情况下，x □ y = 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 ○ 8 ⊗ 1 □ 8\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
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"expression": "1 ○ 8 ⊗ 1 □ 8",
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"operators": null,
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"seed": 87375282,
"simplified_expr": "( ((( 8 + 1)) + (( 1 + 8 / 8 - 8 * 8)) - (( 1 + 8 / 8 - 8 * 8))))",
"solutions_count": null,
"symbol_definitions": {
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"⊗": {
"associativity": "left",
"conditions": [
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"condition": "y是5的倍数",
"operation": " x - (y) / y * 3"
}
],
"default_operation": " (y + x - x)",
"precedence": 4
},
"⊙": null,
"□": {
"associativity": "left",
"conditions": [
{
"condition": "x小于y",
"operation": " y + x"
}
],
"default_operation": " y ⊗ x - x * y",
"precedence": 5
},
"△": null,
"▽": null,
"◇": null,
"○": {
"associativity": "left",
"conditions": [
{
"condition": "x和y都是偶数",
"operation": " x + x * x + y + y"
}
],
"default_operation": " x + y / y - y * y",
"precedence": 5
},
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "8c46812f-e869-4517-aa86-5e7b741203e2"
},
"seed": 87375282,
"task_id": 287375282,
"task_type": "operation"
} |
logic-v2 | Define ▽, the rules are as follows:
when x and y are both odd, x ▽ y = abs(x / y - x);
otherwise, x ▽ y = 4 * x * x / y.
The precedence of operations: ▽ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 6 ▽ 4 % 1
Please fill your final answer in \boxed{}. | {
"game_data": {
"answer": "0",
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"solutions_count": null,
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"▽": {
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"conditions": [
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"default_operation": " 4 * x * x / y",
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"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
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"target": null,
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"trace_id": "f1cbff62-1d20-4a06-b88d-ac1952e857f4"
},
"question": "Define ▽, the rules are as follows:\nwhen x and y are both odd, x ▽ y = abs(x / y - x);\notherwise, x ▽ y = 4 * x * x / y.\nThe precedence of operations: ▽ > ** > * = / = % > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 6 ▽ 4 % 1\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
"closing_sequence": null,
"expression": "6 ▽ 4 % 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null,
"num_of_numbers": null,
"num_symbols": 1,
"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 96710081,
"simplified_expr": "((( 4 * 6 * 6 / 4)) % 1)",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": null,
"▽": {
"associativity": "left",
"conditions": [
{
"condition": "x和y都是奇数",
"operation": " abs(x / y - x)"
}
],
"default_operation": " 4 * x * x / y",
"precedence": 4
},
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "f1cbff62-1d20-4a06-b88d-ac1952e857f4"
},
"seed": 96710081,
"task_id": 296710081,
"task_type": "operation"
} |
logic-v2 | Define ◇, the rules are as follows:
when x is equal to y, 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
Please fill your final answer in \boxed{}. | {
"game_data": {
"answer": "2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2",
"fill_length": null,
"full_sequence": null,
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"language": "english",
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"nesting_depth": null,
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"operators": null,
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"seed": 34177713,
"simplified_expr": "2",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": {
"associativity": "left",
"conditions": [
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],
"default_operation": " x - y * x",
"precedence": 3
},
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
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"trace_id": "8146d2c0-929b-431e-9091-3cb917360f11"
},
"question": "Define ◇, the rules are as follows:\nwhen x is equal to y, 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\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
"closing_sequence": null,
"expression": "2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
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"num_of_numbers": null,
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"numbers": null,
"operators": null,
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"simplified_expr": "2",
"solutions_count": null,
"symbol_definitions": {
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"⊗": null,
"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": {
"associativity": "left",
"conditions": [
{
"condition": "x等于y",
"operation": " x / x * y"
}
],
"default_operation": " x - y * x",
"precedence": 3
},
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
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"trace_id": "8146d2c0-929b-431e-9091-3cb917360f11"
},
"seed": 34177713,
"task_id": 234177713,
"task_type": "operation"
} |
logic-v2 | 定义 ☆，规则如下：
当x和y的和是奇数时，x ☆ y = y - 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 - y + 2 * x。
运算优先级：** = ☆ > * = / = % = ⊗ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 ⊗ 7 ⊗ 8 ☆ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-49",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ⊗ 7 ⊗ 8 ☆ 7",
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"numbers": null,
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"solutions_count": null,
"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 + x * x"
}
],
"default_operation": " x - y * x",
"precedence": 3
},
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "c0d49929-bec8-49d2-acee-080264720e8c"
},
"question": "定义 ☆，规则如下：\n当x和y的和是奇数时，x ☆ y = y - 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 - y + 2 * 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 ⊗ 7 ⊗ 8 ☆ 7\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
"closing_sequence": null,
"expression": "4 ⊗ 7 ⊗ 8 ☆ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
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"num_of_numbers": null,
"num_symbols": 2,
"numbers": null,
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"seed": 17577343,
"simplified_expr": "( (( 4 - 7 + 2 * 4)) - (( 7 - 7 + 8 * 8)) + 2 * (( 4 - 7 + 2 * 4)))",
"solutions_count": null,
"symbol_definitions": {
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"precedence": 2
},
"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": {
"associativity": "left",
"conditions": [
{
"condition": "x和y的和是奇数",
"operation": " y - y + x * x"
}
],
"default_operation": " x - y * x",
"precedence": 3
},
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "c0d49929-bec8-49d2-acee-080264720e8c"
},
"seed": 17577343,
"task_id": 217577343,
"task_type": "operation"
} |
logic-v2 | Define ▽, the rules are as follows:
on the real number field, x ▽ y = 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: 8 ▽ 2 ▽ 2
Please fill your final answer in \boxed{}. | {
"game_data": {
"answer": "4",
"difficulty": 1,
"gpt_response": "",
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"expression": "8 ▽ 2 ▽ 2",
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"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": null,
"▽": {
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"default_operation": " x - x + y + y",
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},
"◇": null,
"○": null,
"◎": null,
"☆": null,
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"♢": null
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"question": "Define ▽, the rules are as follows:\non the real number field, x ▽ y = x - 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: 8 ▽ 2 ▽ 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 * (y / 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 ⊗ 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 ☆ 5 ◎ 4
请将最终答案填入\boxed{}中。 | {
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"question": "定义 ⊗，规则如下：\n实数域上，x ⊗ y = y * (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实数域上，x ☆ y = y ** x ⊗ x。\n运算优先级：** = ⊗ = ◎ > * = / = % > + = - = ☆。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 5 ⊗ 10 ☆ 5 ◎ 4\n请将最终答案填入\\boxed{}中。"
},
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"precedence": 1
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"seed": 6053027,
"task_id": 206053027,
"task_type": "operation"
} |
logic-v2 | 定义 ◇，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 = x + y ** x + y。
运算优先级：** = ◇ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 ◇ 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是偶数时，x △ y = y - x * x；
其他情况下，x △ y = (x - y) * y。
和 ⊗，规则如下：
当x和y都是偶数时，x ⊗ y = x + (y * y)；
其他情况下，x ⊗ y = x △ y。
和 ♢，规则如下：
当x和y都是奇数时，x ♢ y = x ⊗ y；
其他情况下，x ♢ y = x △ y * y。
运算优先级：♢ > ** > * = / = % = △ = ⊗ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ⊗ 2 ⊗ 4 ♢ 5 △ 9
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是5的倍数时，x □ y = y / x；
其他情况下，x □ y = y / x - 5。
和 ♡，规则如下：
当x是偶数时，x ♡ y = y * x；
其他情况下，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 ♡ 7 □ 6
请将最终答案填入\boxed{}中。 | {
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"♢": null
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},
"metadata": {
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"numbers": null,
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"○": null,
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"seed": 93852903,
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} |
logic-v2 | Define □, the rules are as follows:
on the real number field, x □ y = abs(x + y).
and △, the rules are as follows:
when x is less than y, x △ y = abs(y) / x;
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: 8 △ 8 □ 8 △ 2
Please fill your final answer in \boxed{}. | {
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"simplified_expr": "( abs((( 8 + 8 * 8)) + (( 8 + 8 * 2))))",
"solutions_count": null,
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"⊗": null,
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"operation": " abs(y) / x"
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"seed": 91931601,
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} |
logic-v2 | Define ○, the rules are as follows:
when x and y are both even, x ○ y = y + 4 * x;
otherwise, x ○ y = x * 1 - 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: 1 ○ 5
Please fill your final answer in \boxed{}. | {
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"seed": 85565197,
"simplified_expr": "( 1 * 1 - 5 - 1)",
"solutions_count": null,
"symbol_definitions": {
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"□": null,
"△": null,
"▽": null,
"◇": null,
"○": {
"associativity": "left",
"conditions": [
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"condition": "x和y都是偶数",
"operation": " y + 4 * x"
}
],
"default_operation": " x * 1 - y - x",
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},
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"☆": null,
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},
"target": null,
"total_length": null,
"trace_id": "b04128d6-2a47-4966-8b7f-60a84dc3d4e9"
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"question": "Define ○, the rules are as follows:\nwhen x and y are both even, x ○ y = y + 4 * x;\notherwise, x ○ y = x * 1 - 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: 1 ○ 5\nPlease fill your final answer in \\boxed{}."
},
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"○": {
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"conditions": [
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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 + y；
其他情况下，x ⊙ y = y - x - x - y。
和 □，规则如下：
当x等于y时，x □ y = y - 2 - 4 / x；
其他情况下，x □ y = (y ⊙ x) + 5 + 1。
和 ◇，规则如下：
当y是偶数时，x ◇ y = y + 1 - 3 / x；
其他情况下，x ◇ y = x * y □ x。
运算优先级：** = ⊙ > * = / = % = ◇ > + = - = □。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 ⊙ 4 □ 4
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当x和y的和是偶数时，x ⊙ y = x / x + y；\n其他情况下，x ⊙ y = y - x - x - y。\n和 □，规则如下：\n当x等于y时，x □ y = y - 2 - 4 / x；\n其他情况下，x □ y = (y ⊙ x) + 5 + 1。\n和 ◇，规则如下：\n当y是偶数时，x ◇ y = y + 1 - 3 / x；\n其他情况下，x ◇ y = x * y □ x。\n运算优先级：** = ⊙ > * = / = % = ◇ > + = - = □。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 4 ⊙ 4 □ 4\n请将最终答案填入\\boxed{}中。"
},
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"default_operation": " y - x - x - y",
"precedence": 3
},
"□": {
"associativity": "left",
"conditions": [
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"condition": "x等于y",
"operation": " y - 2 - 4 / x"
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"default_operation": " (y ⊙ x) + 5 + 1",
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"operation": " y + 1 - 3 / x"
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"♢": null
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},
"seed": 3477036,
"task_id": 203477036,
"task_type": "operation"
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logic-v2 | Define ◇, the rules are as follows:
when x and y are both odd, x ◇ y = y + 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: 5 + 6 ◇ 3 ◇ 2
Please fill your final answer in \boxed{}. | {
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"question": "Define ◇, the rules are as follows:\nwhen x and y are both odd, x ◇ y = y + 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: 5 + 6 ◇ 3 ◇ 2\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
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"expression": "5 + 6 ◇ 3 ◇ 2",
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"seed": 9927592,
"simplified_expr": "(5 + (( (( 6 / 3 - 6)) / 2 - (( 6 / 3 - 6)))))",
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"seed": 9927592,
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} |
logic-v2 | Define ☆, the rules are as follows:
on the real number field, x ☆ y = 4 + abs(y) / x.
and ♢, the rules are as follows:
on the real number field, 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: 1 ♢ 9 ☆ 7
Please fill your final answer in \boxed{}. | {
"game_data": {
"answer": "4.0875",
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"♡": null,
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"associativity": "left",
"conditions": [],
"default_operation": " y * y - x",
"precedence": 5
}
},
"target": null,
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"trace_id": "ae857615-268a-404b-9655-ee4492cbc926"
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"question": "Define ☆, the rules are as follows:\non the real number field, x ☆ y = 4 + abs(y) / x.\nand ♢, the rules are as follows:\non the real number field, 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: 1 ♢ 9 ☆ 7\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
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"expression": "1 ♢ 9 ☆ 7",
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"seed": 18852182,
"simplified_expr": "( 4 + abs(7) / (( 9 * 9 - 1)))",
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"◎": null,
"☆": {
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"♡": null,
"♢": {
"associativity": "left",
"conditions": [],
"default_operation": " y * y - x",
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},
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},
"seed": 18852182,
"task_id": 218852182,
"task_type": "operation"
} |
logic-v2 | Define △, the rules are as follows:
when y is even, x △ y = x - y * x;
otherwise, x △ y = abs(y + x + x).
The precedence of operations: ** = △ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 4 △ 10
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是奇数时，x □ y = y * (x) - 5；
其他情况下，x □ y = y + abs(y + y) + x。
和 ☆，规则如下：
当x和y的和是偶数时，x ☆ y = y * x - abs(x) * x；
其他情况下，x ☆ y = x □ x - y - 1。
运算优先级：** = □ > * = / = % = ☆ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 □ 7 ☆ 4
请将最终答案填入\boxed{}中。 | {
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"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": {
"associativity": "left",
"conditions": [
{
"condition": "x和y的和是偶数",
"operation": " y * x - abs(x) * x"
}
],
"default_operation": " x □ x - y - 1",
"precedence": 2
},
"♡": null,
"♢": null
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"target": null,
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"trace_id": "7297442c-9da7-45fc-ac07-0fd7bf3679ab"
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"question": "定义 □，规则如下：\n当y是奇数时，x □ y = y * (x) - 5；\n其他情况下，x □ y = y + abs(y + y) + x。\n和 ☆，规则如下：\n当x和y的和是偶数时，x ☆ y = y * x - abs(x) * x；\n其他情况下，x ☆ y = x □ x - y - 1。\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 ☆ 4\n请将最终答案填入\\boxed{}中。"
},
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"operation": " y * (x) - 5"
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},
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": {
"associativity": "left",
"conditions": [
{
"condition": "x和y的和是偶数",
"operation": " y * x - abs(x) * x"
}
],
"default_operation": " x □ x - y - 1",
"precedence": 2
},
"♡": null,
"♢": null
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logic-v2 | 定义 □，规则如下：
实数域上，x □ y = y + y - y - x + x。
和 ⊗，规则如下：
当x是偶数时，x ⊗ y = y ** x + 5 ** y ** y；
其他情况下，x ⊗ y = y □ x。
和 △，规则如下：
实数域上，x △ y = x * 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 △ 5 □ 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和y的和是奇数时，x ⊕ y = 2 - y * x - y / 2；
其他情况下，x ⊕ y = y - x - y + y - x。
和 ◎，规则如下：
当x小于y时，x ◎ y = (x + y + y) + 2；
其他情况下，x ◎ y = y ⊕ x / y + x。
和 □，规则如下：
当x和y都是偶数时，x □ y = y / y / x - 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: 9 ⊕ 5 □ 8 ◎ 5 ⊕ 4
请将最终答案填入\boxed{}中。 | {
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logic-v2 | 定义 ⊗，规则如下：
实数域上，x ⊗ y = y + x * y * abs(y)。
和 ♢，规则如下：
实数域上，x ♢ y = x + x + y - abs(y)。
和 ○，规则如下：
实数域上，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: 3 ♢ 10 ⊗ 6
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logic-v2 | 定义 ☆，规则如下：
实数域上，x ☆ y = x - y + x。
和 ♡，规则如下：
当x是偶数时，x ♡ y = 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: 4 ☆ 10 ♡ 1 * 9
请将最终答案填入\boxed{}中。 | {
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logic-v2 | 定义 □，规则如下：
实数域上，x □ y = x * 2 - y * y + 1。
和 ▽，规则如下：
当y是奇数时，x ▽ y = y * x；
其他情况下，x ▽ y = y + y + 3 / x。
运算优先级：** > * = / = % > + = - = □ = ▽。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 / 1 ** 3 □ 2 ▽ 10
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 + abs(y * x) - y。
和 ⊗，规则如下：
当y是3的倍数时，x ⊗ y = y + abs(x)；
其他情况下，x ⊗ y = (x ** x) ♢ y * x。
和 ☆，规则如下：
实数域上，x ☆ y = y / x ⊗ 4 * 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 ⊗ 3 ⊗ 9 ♢ 9 ☆ 6
请将最终答案填入\boxed{}中。 | {
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"conditions": [
{
"condition": "y是3的倍数",
"operation": " y + abs(x)"
}
],
"default_operation": " (x ** x) ♢ y * x",
"precedence": 3
},
"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": {
"associativity": "left",
"conditions": [],
"default_operation": " y / x ⊗ 4 * x",
"precedence": 5
},
"♡": null,
"♢": {
"associativity": "left",
"conditions": [],
"default_operation": " y + abs(y * x) - y",
"precedence": 3
}
},
"target": null,
"total_length": null,
"trace_id": "c93048eb-049b-4d55-9261-3780ade24432"
},
"question": "定义 ♢，规则如下：\n实数域上，x ♢ y = y + abs(y * x) - y。\n和 ⊗，规则如下：\n当y是3的倍数时，x ⊗ y = y + abs(x)；\n其他情况下，x ⊗ y = (x ** x) ♢ y * x。\n和 ☆，规则如下：\n实数域上，x ☆ y = y / x ⊗ 4 * 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 ⊗ 3 ⊗ 9 ♢ 9 ☆ 6\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
"closing_sequence": null,
"expression": "9 ⊗ 3 ⊗ 9 ♢ 9 ☆ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null,
"num_of_numbers": null,
"num_symbols": 3,
"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 59065817,
"simplified_expr": "( (((((6 / ((((( 4 + abs(4 * ((9 ** 9))) - 4)) * 9))))) * 9))) + abs((((((6 / ((((( 4 + abs(4 * ((9 ** 9))) - 4)) * 9))))) * 9))) * (( 9 + abs((( 3 + abs(9))))))) - (((((6 / ((((( 4 + abs(4 * ((9 ** 9))) - 4)) * 9))))) * 9))))",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": {
"associativity": "left",
"conditions": [
{
"condition": "y是3的倍数",
"operation": " y + abs(x)"
}
],
"default_operation": " (x ** x) ♢ y * x",
"precedence": 3
},
"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": {
"associativity": "left",
"conditions": [],
"default_operation": " y / x ⊗ 4 * x",
"precedence": 5
},
"♡": null,
"♢": {
"associativity": "left",
"conditions": [],
"default_operation": " y + abs(y * x) - y",
"precedence": 3
}
},
"target": null,
"total_length": null,
"trace_id": "c93048eb-049b-4d55-9261-3780ade24432"
},
"seed": 59065817,
"task_id": 259065817,
"task_type": "operation"
} |
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