env stringclasses 1
value | prompt stringlengths 119 673 | extra dict |
|---|---|---|
logic-v2 | Define ◇, the rules are as follows:
when y is a multiple of 5, x ◇ y = y - y + y + x;
otherwise, x ◇ y = x - y + abs(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 = 3 + y * 4 - 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: 5 ◎ 2 ☆ 3 ◇ 8
Please fill your final answer in \boxed{}. | {
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"precedence": 1
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"question": "Define ◇, the rules are as follows:\nwhen y is a multiple of 5, x ◇ y = y - y + y + x;\notherwise, x ◇ y = x - y + abs(y).\nand ☆, 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 = 3 + y * 4 - x + 1.\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 ◎ 2 ☆ 3 ◇ 8\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 / 5 - 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 ○ 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 + x / 5 - 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 ○ 2\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 + 5 / y * x。
和 ☆，规则如下：
实数域上，x ☆ y = x ♢ x - x + y * 4。
和 ▽，规则如下：
当x大于y时，x ▽ y = y ** x + y + y * x；
其他情况下，x ▽ y = x * y + (3)。
运算优先级：☆ > ** = ♢ > * = / = % > + = - = ▽。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ☆ 4 ♢ 2 ▽ 4
请将最终答案填入\boxed{}中。 | {
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"simplified_expr": "( (( ((((((( 1 + 5 / 1 * 1)) - 1)) + ((4 * 4))))) + 5 / 2 * ((((((( 1 + 5 / 1 * 1)) - 1)) + ((4 * 4))))))) * 4 + (3))",
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"question": "定义 ♢，规则如下：\n实数域上，x ♢ y = x + 5 / y * x。\n和 ☆，规则如下：\n实数域上，x ☆ y = x ♢ x - x + y * 4。\n和 ▽，规则如下：\n当x大于y时，x ▽ y = y ** x + y + y * x；\n其他情况下，x ▽ y = x * y + (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: 1 ☆ 4 ♢ 2 ▽ 4\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 + 1；
其他情况下，x ♢ y = (x - y / y)。
和 ⊕，规则如下：
实数域上，x ⊕ y = 4 * (y) - x。
和 ♡，规则如下：
当y是偶数时，x ♡ y = y - x + x；
其他情况下，x ♡ y = x ♢ y。
运算优先级：** = ⊕ = ♡ > * = / = % > + = - = ♢。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 ♢ 10 ⊕ 3 ♡ 10
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 = abs(5 * y) + x；
其他情况下，x ⊕ y = y / (3) / x。
和 ◎，规则如下：
实数域上，x ◎ y = x * y + x。
和 △，规则如下：
实数域上，x △ y = x ◎ 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 ⊕ 4 △ 10 ◎ 1
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 - 3 + (y + y / y)。
和 □，规则如下：
实数域上，x □ y = y * (y - 3) * x。
和 ◎，规则如下：
实数域上，x ◎ y = y * y + x。
运算优先级：□ > ** = ⊕ > * = / = % > + = - = ◎。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 □ 10 ◎ 6 ⊕ 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 = x - 3 + (y + y / y)。\n和 □，规则如下：\n实数域上，x □ y = y * (y - 3) * x。\n和 ◎，规则如下：\n实数域上，x ◎ y = y * y + x。\n运算优先级：□ > ** = ⊕ > * = / = % > + = - = ◎。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 4 □ 10 ◎ 6 ⊕ 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 = x - x - y。
和 ○，规则如下：
实数域上，x ○ y = x - x - 1 - y。
和 ▽，规则如下：
实数域上，x ▽ y = y + y + y + x。
运算优先级：⊕ = ○ > ** = ▽ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 ⊕ 1 ○ 9 ▽ 3
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 * 1。
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 ◎ 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 = 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 / 1 △ 10
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 - 5；
其他情况下，x ◎ y = y * 1 + x * x。
和 ⊗，规则如下：
当x是3的倍数时，x ⊗ y = y * x ◎ 1；
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: 1 ◎ 6
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 + 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 ○ 3 % 10 ** 9
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 + 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 * 1 △ 8
Please fill your final answer in \boxed{}. | {
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logic-v2 | 定义 ◎，规则如下：
实数域上，x ◎ y = x + (x - x) + y / y。
和 ⊕，规则如下：
实数域上，x ⊕ y = y * 5 + x ◎ y。
和 ♡，规则如下：
当x和y都是偶数时，x ♡ y = abs(y - x / y) + 3；
其他情况下，x ♡ y = (4 - 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 ♡ 7 ⊕ 1 ◎ 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等于y时，x ◎ y = y - x + y - 1 / x；
其他情况下，x ◎ y = y * 4 - x。
和 ⊙，规则如下：
当x和y都是奇数时，x ⊙ y = x * x - y * y ◎ x；
其他情况下，x ⊙ y = (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: 6 ◎ 3 ⊙ 2
请将最终答案填入\boxed{}中。 | {
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"default_operation": " y * 4 - x",
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"trace_id": "72f81e83-a8ff-4cd7-990b-72b3ced3c027"
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"question": "定义 ◎，规则如下：\n当x等于y时，x ◎ y = y - x + y - 1 / x；\n其他情况下，x ◎ y = y * 4 - x。\n和 ⊙，规则如下：\n当x和y都是奇数时，x ⊙ y = x * x - y * y ◎ x；\n其他情况下，x ⊙ y = (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: 6 ◎ 3 ⊙ 2\n请将最终答案填入\\boxed{}中。"
},
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],
"default_operation": " y * 4 - x",
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"☆": null,
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"seed": 46651777,
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logic-v2 | Define ▽, the rules are as follows:
when x is odd, x ▽ y = x * x ** y - x * x;
otherwise, 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: 1
Please fill your final answer in \boxed{}. | {
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"question": "Define ▽, the rules are as follows:\nwhen x is odd, x ▽ y = x * x ** y - x * x;\notherwise, 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: 1\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
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"expression": "1",
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"⊙": null,
"□": null,
"△": null,
"▽": {
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"conditions": [
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"operation": " x * x ** y - x * x"
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],
"default_operation": " y ** x - x + y - y",
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},
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
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"seed": 80682903,
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logic-v2 | 定义 ◇，规则如下：
当x和y都是偶数时，x ◇ y = abs(4 * x) - y；
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: 3 - 5 % 7 ◇ 10
请将最终答案填入\boxed{}中。 | {
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"question": "定义 ◇，规则如下：\n当x和y都是偶数时，x ◇ y = abs(4 * x) - y；\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: 3 - 5 % 7 ◇ 10\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
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"expression": "3 - 5 % 7 ◇ 10",
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"simplified_expr": "( abs(4 * ((3 - ((5 % 7))))) - 10)",
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"seed": 42783735,
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logic-v2 | Define ⊗, the rules are as follows:
on the real number field, x ⊗ y = 3 * abs(x) - y.
and ○, the rules are as follows:
on the real number field, x ○ y = abs(y) / x.
and □, the rules are as follows:
when x is less than y, x □ y = abs(x - y + y);
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: 5 ○ 4 □ 2 ⊗ 7
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:\non the real number field, x ⊗ y = 3 * abs(x) - y.\nand ○, the rules are as follows:\non the real number field, x ○ y = abs(y) / x.\nand □, the rules are as follows:\nwhen x is less than y, x □ y = abs(x - y + y);\notherwise, x □ y = (y ** x) * y.\nThe precedence of operations: ** = □ > * = / = % = ○ > + = - = ⊗。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 5 ○ 4 □ 2 ⊗ 7\nPlease fill your final answer in \\boxed{}."
},
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"expression": "5 ○ 4 □ 2 ⊗ 7",
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"associativity": "left",
"conditions": [
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"condition": "x小于y",
"operation": " abs(x - y + y)"
}
],
"default_operation": " (y ** x) * y",
"precedence": 3
},
"△": null,
"▽": null,
"◇": null,
"○": {
"associativity": "left",
"conditions": [],
"default_operation": " abs(y) / x",
"precedence": 2
},
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "549e0f75-aab0-4b3c-b8a6-c75b589cf0a3"
},
"seed": 78953607,
"task_id": 278953607,
"task_type": "operation"
} |
logic-v2 | 定义 ♢，规则如下：
当x和y都是奇数时，x ♢ y = x + y - x；
其他情况下，x ♢ y = x * y * 3。
和 ♡，规则如下：
实数域上，x ♡ y = x + (x * y)。
和 ▽，规则如下：
当x大于y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: 5 ♢ 5 ▽ 10 ♡ 10 ▽ 8
请将最终答案填入\boxed{}中。 | {
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},
"♢": {
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"conditions": [
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"operation": " x + y - x"
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"question": "定义 ♢，规则如下：\n当x和y都是奇数时，x ♢ y = x + y - x；\n其他情况下，x ♢ y = x * y * 3。\n和 ♡，规则如下：\n实数域上，x ♡ y = x + (x * y)。\n和 ▽，规则如下：\n当x大于y时，x ▽ y = x + x - y；\n其他情况下，x ▽ 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 ♢ 5 ▽ 10 ♡ 10 ▽ 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 * x / x;
otherwise, x ☆ y = y - y * x * y + x.
and ○, the rules are as follows:
when x is a multiple of 3, x ○ y = y - y * x + x - y;
otherwise, x ○ y = 5 * 2 ☆ x + y * 2.
The precedence of operations: ○ > ** > * = / = % = ☆ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 9 ☆ 6
Please fill your final answer in \boxed{}. | {
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logic-v2 | 定义 □，规则如下：
当x和y的和是偶数时，x □ y = y - x * y * y - y；
其他情况下，x □ y = 4 + y - x / 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: 10 □ 2 ◇ 1
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的和是偶数时，x □ y = y - x * y * y - y；\n其他情况下，x □ y = 4 + y - x / y / x。\n和 ◇，规则如下：\n实数域上，x ◇ y = x + (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: 10 □ 2 ◇ 1\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 = abs(y) + y - x。
和 ☆，规则如下：
实数域上，x ☆ y = x - y - y。
和 ♡，规则如下：
实数域上，x ♡ y = y * y + x。
运算优先级：☆ > ** > * = / = % > + = - = ⊗ = ♡。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 9 ⊗ 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y是奇数时，x ○ y = (x - x + y) + y；
其他情况下，x ○ y = y * y - x。
和 ♢，规则如下：
当y是3的倍数时，x ♢ y = (y ○ x - x)；
其他情况下，x ♢ y = abs(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: 7 ○ 3 ♢ 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都是奇数时，x ⊕ y = 2 * x - y - 2；
其他情况下，x ⊕ y = 4 + 3 * x - y。
和 ⊙，规则如下：
实数域上，x ⊙ y = (y) ⊕ x。
和 ⊗，规则如下：
实数域上，x ⊗ y = y + x / x * x。
运算优先级：⊕ = ⊙ > ** = ⊗ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7 ⊙ 3 ⊗ 3 ⊕ 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 = y / 4 * x.
and △, 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: 4 △ 6 □ 5
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 - 2 + x - abs(2 + y);
otherwise, x ⊕ y = x * y - x - x + y.
and □, the rules are as follows:
when x and y are both even, x □ y = y - (y ⊕ x / x);
otherwise, x □ y = x + y.
and ☆, the rules are as follows:
when y is a multiple of 3, x ☆ y = (y + 3 - y + y □ x);
otherwise, x ☆ y = (y ⊕ x - 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: 8 ⊕ 1 ☆ 2 □ 2
Please fill your final answer in \boxed{}. | {
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"▽": null,
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"♢": null
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"question": "Define ⊕, the rules are as follows:\nwhen x is a multiple of 5, x ⊕ y = x - 2 + x - abs(2 + y);\notherwise, x ⊕ y = x * y - x - x + y.\nand □, the rules are as follows:\nwhen x and y are both even, x □ y = y - (y ⊕ x / x);\notherwise, x □ y = x + y.\nand ☆, the rules are as follows:\nwhen y is a multiple of 3, x ☆ y = (y + 3 - y + y □ x);\notherwise, x ☆ y = (y ⊕ x - 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: 8 ⊕ 1 ☆ 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 = 4 + y + y + x。
和 △，规则如下：
当x和y都是奇数时，x △ y = (y ♡ x) * x * y；
其他情况下，x △ y = y + x - x ♡ x。
运算优先级：** > * = / = % = △ > + = - = ♡。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 △ 6 ♡ 1
请将最终答案填入\boxed{}中。 | {
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"♢": null
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"question": "定义 ♡，规则如下：\n实数域上，x ♡ y = 4 + y + y + x。\n和 △，规则如下：\n当x和y都是奇数时，x △ y = (y ♡ x) * x * y；\n其他情况下，x △ y = y + x - x ♡ x。\n运算优先级：** > * = / = % = △ > + = - = ♡。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 6 △ 6 ♡ 1\n请将最终答案填入\\boxed{}中。"
},
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"seed": 25930287,
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} |
logic-v2 | Define □, the rules are as follows:
when x is even, x □ y = y ** x;
otherwise, x □ y = abs(x) + y.
and ♢, the rules are as follows:
when the sum of x and y is even, x ♢ y = x □ y + 2;
otherwise, x ♢ y = x * y * y.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = x + y / y.
The precedence of operations: □ > ** > * = / = % = ♢ > + = - = ⊗。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 4 / 3 □ 8 ⊗ 6 ♢ 4
Please fill your final answer in \boxed{}. | {
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"operation": " x □ y + 2"
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},
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"operation": " x □ y + 2"
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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: 6
请将最终答案填入\boxed{}中。 | {
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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 = 5 - y / x + 1。
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: 2 □ 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 = 5 - y / x + 1。\n和 ☆，规则如下：\n实数域上，x ☆ 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: 2 □ 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 = x + x - y + x；
其他情况下，x ○ y = 5 - 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: 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 + 5 + y).
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: 9 ⊗ 10 ☆ 1
Please fill your final answer in \boxed{}. | {
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logic-v2 | 定义 ⊕，规则如下：
实数域上，x ⊕ y = x + x * y / x + x。
和 ♡，规则如下：
实数域上，x ♡ y = y ⊕ x / x。
和 ◎，规则如下：
当y是5的倍数时，x ◎ y = 5 + (x * y - 4)；
其他情况下，x ◎ y = y - x + 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: 9 ◎ 10 ♡ 2
请将最终答案填入\boxed{}中。 | {
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"☆": null,
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"conditions": [],
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"question": "定义 ⊕，规则如下：\n实数域上，x ⊕ y = x + x * y / x + x。\n和 ♡，规则如下：\n实数域上，x ♡ y = y ⊕ x / x。\n和 ◎，规则如下：\n当y是5的倍数时，x ◎ y = 5 + (x * y - 4)；\n其他情况下，x ◎ y = y - x + 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: 9 ◎ 10 ♡ 2\n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 = (y - x + x)；
其他情况下，x ♡ y = x + y - y。
和 ⊕，规则如下：
当x大于y时，x ⊕ y = x - x - y；
其他情况下，x ⊕ y = y * 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: 1 ♡ 7 ** 3 * 8 ⊕ 4
请将最终答案填入\boxed{}中。 | {
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},
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logic-v2 | 定义 ○，规则如下：
当y是5的倍数时，x ○ y = y - y - abs(x) - x - x；
其他情况下，x ○ y = (x ** x + x + x - y)。
和 ▽，规则如下：
当x和y都是偶数时，x ▽ y = x + x ○ y / x；
其他情况下，x ▽ y = x + y - y / y - y。
和 ♢，规则如下：
实数域上，x ♢ y = x ** 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: 4 % 1 ○ 5 ♢ 5 ▽ 3
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 * 5 * y + x - 2;
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: 1 % 7 ♢ 10
Please fill your final answer in \boxed{}. | {
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},
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"○": null,
"◎": null,
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"♡": null,
"♢": {
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"operation": " x * 5 * y + x - 2"
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} |
logic-v2 | Define ○, the rules are as follows:
when x is a multiple of 3, x ○ y = y ** x * abs(3) - y;
otherwise, 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: 1 ○ 2 + 1
Please fill your final answer in \boxed{}. | {
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"simplified_expr": "((( 1 + 1 * 2 / 1)) + 1)",
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"♢": null
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"question": "Define ○, the rules are as follows:\nwhen x is a multiple of 3, x ○ y = y ** x * abs(3) - y;\notherwise, 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: 1 ○ 2 + 1\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
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"expression": "1 ○ 2 + 1",
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"seed": 51660785,
"simplified_expr": "((( 1 + 1 * 2 / 1)) + 1)",
"solutions_count": null,
"symbol_definitions": {
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"△": null,
"▽": null,
"◇": null,
"○": {
"associativity": "left",
"conditions": [
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"condition": "x是3的倍数",
"operation": " y ** x * abs(3) - y"
}
],
"default_operation": " x + x * y / x",
"precedence": 2
},
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
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},
"seed": 51660785,
"task_id": 251660785,
"task_type": "operation"
} |
logic-v2 | Define ▽, the rules are as follows:
on the real number field, x ▽ y = x + abs(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 ▽ 9
Please fill your final answer in \boxed{}. | {
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"answer": "18",
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"gpt_response": "",
"metadata": {
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"expression": "9 ▽ 9",
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"question": "Define ▽, the rules are as follows:\non the real number field, x ▽ y = x + abs(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 ▽ 9\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
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"expression": "9 ▽ 9",
"fill_length": null,
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"solutions_count": null,
"symbol_definitions": {
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"⊗": null,
"⊙": null,
"□": null,
"△": null,
"▽": {
"associativity": "left",
"conditions": [],
"default_operation": " x + abs(y - x + y)",
"precedence": 2
},
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
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},
"seed": 98928322,
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"task_type": "operation"
} |
logic-v2 | 定义 ⊗，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 - 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 % 7 ⊗ 3 / 7
请将最终答案填入\boxed{}中。 | {
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"question": "定义 ⊗，规则如下：\n当x是5的倍数时，x ⊗ y = y * 3 - x；\n其他情况下，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: 1 % 7 ⊗ 3 / 7\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
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},
"seed": 16851632,
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"task_type": "operation"
} |
logic-v2 | 定义 ☆，规则如下：
当x是奇数时，x ☆ y = y - y * x；
其他情况下，x ☆ y = y + (x * y)。
和 ⊙，规则如下：
当x是奇数时，x ⊙ y = y - (x * 3)；
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: 9 ☆ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-40",
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"gpt_response": "",
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"▽": null,
"◇": null,
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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当x是奇数时，x ☆ y = y - y * x；\n其他情况下，x ☆ y = y + (x * y)。\n和 ⊙，规则如下：\n当x是奇数时，x ⊙ y = y - (x * 3)；\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: 9 ☆ 5\n请将最终答案填入\\boxed{}中。"
},
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],
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},
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"○": null,
"◎": null,
"☆": {
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{
"condition": "x是奇数",
"operation": " y - y * x"
}
],
"default_operation": " y + (x * y)",
"precedence": 1
},
"♡": null,
"♢": null
},
"target": null,
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},
"seed": 56517259,
"task_id": 256517259,
"task_type": "operation"
} |
logic-v2 | Define ◇, the rules are as follows:
on the real number field, x ◇ y = x ** y * 4 * 2 * 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: 8
Please fill your final answer in \boxed{}. | {
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},
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"△": null,
"▽": null,
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"associativity": "left",
"conditions": [],
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"precedence": 1
},
"○": null,
"◎": null,
"☆": null,
"♡": null,
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},
"target": null,
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"seed": 36916778,
"task_id": 236916778,
"task_type": "operation"
} |
logic-v2 | Define ⊗, the rules are as follows:
on the real number field, x ⊗ y = x * abs(y * y).
and ⊙, 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 = 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 ⊗ 4 ▽ 4 ⊙ 9
Please fill your final answer in \boxed{}. | {
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"precedence": 5
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"□": null,
"△": null,
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"conditions": [],
"default_operation": " x + x * y",
"precedence": 5
},
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
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"trace_id": "47eefd6c-8eef-4ec6-8a92-bc2caf08df5a"
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"question": "Define ⊗, the rules are as follows:\non the real number field, x ⊗ y = x * abs(y * y).\nand ⊙, the rules are as follows:\non the real number field, x ⊙ y = x / y ** 1.\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: 8 ⊗ 4 ▽ 4 ⊙ 9\nPlease fill your final answer in \\boxed{}."
},
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"numbers": null,
"operators": null,
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"seed": 48524038,
"simplified_expr": "( 8 * abs((( (( 4 + 4 * 4)) / 9 ** 1)) * (( (( 4 + 4 * 4)) / 9 ** 1))))",
"solutions_count": null,
"symbol_definitions": {
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"conditions": [],
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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 = y - y / x;
otherwise, x ☆ y = y - x - x.
and ◎, the rules are as follows:
when x is odd, x ◎ y = x + 3 ☆ 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: 3 ☆ 2
Please fill your final answer in \boxed{}. | {
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"operation": " y - y / x"
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"default_operation": " y - x - x",
"precedence": 1
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"♡": null,
"♢": null
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"operation": " y - y / x"
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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和y都是偶数时，x ⊗ y = 5 ⊕ y + y * x；
其他情况下，x ⊗ y = y ⊕ (x / y)。
和 □，规则如下：
当y是5的倍数时，x □ y = y - y + x；
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: 3 □ 8 ⊕ 4
请将最终答案填入\boxed{}中。 | {
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},
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"operation": " 5 ⊕ y + y * x"
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],
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logic-v2 | Define ⊗, the rules are as follows:
when y is even, x ⊗ y = x / y ** y * x;
otherwise, x ⊗ y = y * x - x + y.
and ○, the rules are as follows:
on the real number field, x ○ y = y - y ⊗ (x) * x.
and ♢, the rules are as follows:
when y is even, x ♢ y = (x ** y + 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: 5 ♢ 8 ○ 2 ⊗ 10 - 2 ⊗ 1
Please fill your final answer in \boxed{}. | {
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"□": null,
"△": null,
"▽": null,
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},
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"conditions": [
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"operation": " (x ** y + y) + x"
}
],
"default_operation": " y / y * x ○ (x)",
"precedence": 2
}
},
"target": null,
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"trace_id": "dc534d1b-139d-4b90-bded-db2b96ee54ae"
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"question": "Define ⊗, the rules are as follows:\nwhen y is even, x ⊗ y = x / y ** y * x;\notherwise, x ⊗ y = y * x - x + y.\nand ○, the rules are as follows:\non the real number field, x ○ y = y - y ⊗ (x) * x.\nand ♢, the rules are as follows:\nwhen y is even, x ♢ y = (x ** y + 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: 5 ♢ 8 ○ 2 ⊗ 10 - 2 ⊗ 1\nPlease fill your final answer in \\boxed{}."
},
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"simplified_expr": "((( 10 * (((((((2 - ((((((2 / ((8 ** 8)))) * 2)) * 8)))) / ((2 - ((((((2 / ((8 ** 8)))) * 2)) * 8)))))) * (((5 - (((( 5 * 5 - 5 + 5)) * 5)))))))) - (((((((2 - ((((((2 / ((8 ** 8)))) * 2)) * 8)))) / ((2 - ((((((2 / ((8 ** 8)))) * 2)) * 8)))))) * (((5 - (((( 5 * 5 - 5 + 5)) * 5)))))))) + 10)) - (( 1 * 2 - 2 + 1)))",
"solutions_count": null,
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},
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"operation": " (x ** y + y) + x"
}
],
"default_operation": " y / y * x ○ (x)",
"precedence": 2
}
},
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},
"seed": 638316,
"task_id": 200638316,
"task_type": "operation"
} |
logic-v2 | Define ◇, the rules are as follows:
on the real number field, x ◇ y = y - x - abs(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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"question": "Define ◇, the rules are as follows:\non the real number field, x ◇ y = y - x - abs(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": {
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"expression": "6 ◇ 5",
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"△": null,
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"◎": null,
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logic-v2 | Define ⊙, the rules are as follows:
when x is a multiple of 5, x ⊙ y = x - (y) / y;
otherwise, x ⊙ y = x * x * y.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = 2 + y * x.
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 ○ 6 ⊗ 8
Please fill your final answer in \boxed{}. | {
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"△": null,
"▽": null,
"◇": null,
"○": {
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"conditions": [],
"default_operation": " x + x - y",
"precedence": 4
},
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
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"trace_id": "3b2cc33a-9166-4aef-b9fb-04112ae75726"
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"question": "Define ⊙, the rules are as follows:\nwhen x is a multiple of 5, x ⊙ y = x - (y) / y;\notherwise, x ⊙ y = x * x * y.\nand ⊗, the rules are as follows:\non the real number field, x ⊗ y = 2 + y * x.\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 ○ 6 ⊗ 8\nPlease fill your final answer in \\boxed{}."
},
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"simplified_expr": "( 2 + 8 * (( (( 4 * 4 * 10)) + (( 4 * 4 * 10)) - 6)))",
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"symbol_definitions": {
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"⊙": {
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"condition": "x是5的倍数",
"operation": " x - (y) / y"
}
],
"default_operation": " x * x * y",
"precedence": 5
},
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": {
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"default_operation": " x + x - y",
"precedence": 4
},
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
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"trace_id": "3b2cc33a-9166-4aef-b9fb-04112ae75726"
},
"seed": 36497127,
"task_id": 236497127,
"task_type": "operation"
} |
logic-v2 | Define ▽, the rules are as follows:
when x is a multiple of 3, x ▽ y = x + y + 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: 3 ▽ 10 - 2
Please fill your final answer in \boxed{}. | {
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"question": "Define ▽, the rules are as follows:\nwhen x is a multiple of 3, x ▽ y = x + y + 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: 3 ▽ 10 - 2\nPlease fill your final answer in \\boxed{}."
},
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logic-v2 | Define ♡, the rules are as follows:
when y is odd, x ♡ y = x + x + y - x / 1;
otherwise, x ♡ y = x + y - x.
and ○, the rules are as follows:
when x is greater than y, x ○ y = y - x * y / y + y;
otherwise, x ○ y = y - y - x ** (x + x).
The precedence of operations: ○ > ** > * = / = % > + = - = ♡。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 3 ♡ 6 ○ 2
Please fill your final answer in \boxed{}. | {
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"operation": " x + x + y - x / 1"
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"precedence": 1
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"question": "Define ♡, the rules are as follows:\nwhen y is odd, x ♡ y = x + x + y - x / 1;\notherwise, x ♡ y = x + y - x.\nand ○, the rules are as follows:\nwhen x is greater than y, x ○ y = y - x * y / y + y;\notherwise, x ○ y = y - y - x ** (x + x).\nThe precedence of operations: ○ > ** > * = / = % > + = - = ♡。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 3 ♡ 6 ○ 2\nPlease fill your final answer in \\boxed{}."
},
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"condition": "y是奇数",
"operation": " x + x + y - x / 1"
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],
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},
"♢": null
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"seed": 39718886,
"task_id": 239718886,
"task_type": "operation"
} |
logic-v2 | Define ⊙, the rules are as follows:
on the real number field, x ⊙ y = y + 1 + x.
and ◎, the rules are as follows:
when the sum of x and y is odd, x ◎ y = (y ⊙ x) * y;
otherwise, x ◎ y = 1 + abs(y * x).
and □, the rules are as follows:
when y is a multiple of 3, 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: 8 ◎ 3 □ 6
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 + 1 + x.\nand ◎, the rules are as follows:\nwhen the sum of x and y is odd, x ◎ y = (y ⊙ x) * y;\notherwise, x ◎ y = 1 + abs(y * x).\nand □, the rules are as follows:\nwhen y is a multiple of 3, 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: 8 ◎ 3 □ 6\nPlease fill your final answer in \\boxed{}."
},
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},
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"operation": " x * y"
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"operation": " (y ⊙ x) * y"
}
],
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},
"☆": null,
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logic-v2 | Define ⊕, the rules are as follows:
when x is equal to y, x ⊕ y = x + x / y - y * 4;
otherwise, x ⊕ y = x - x - y ** y * y.
and ♡, the rules are as follows:
when the sum of x and y is odd, x ♡ y = x + (3 * 3) - y * 3;
otherwise, x ♡ y = y + y + x + 3 + x.
and ○, the rules are as follows:
when x is a multiple of 5, x ○ y = x * x - x - y;
otherwise, x ○ y = x - y * 5 * 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: 1 ○ 8 ⊕ 9 ♡ 8
Please fill your final answer in \boxed{}. | {
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"△": null,
"▽": null,
"◇": null,
"○": {
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"conditions": [
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"operation": " x * x - x - y"
}
],
"default_operation": " x - y * 5 * 2",
"precedence": 1
},
"◎": null,
"☆": null,
"♡": {
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"conditions": [
{
"condition": "x和y的和是奇数",
"operation": " x + (3 * 3) - y * 3"
}
],
"default_operation": " y + y + x + 3 + x",
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"♢": null
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"question": "Define ⊕, the rules are as follows:\nwhen x is equal to y, x ⊕ y = x + x / y - y * 4;\notherwise, x ⊕ y = x - x - y ** y * y.\nand ♡, the rules are as follows:\nwhen the sum of x and y is odd, x ♡ y = x + (3 * 3) - y * 3;\notherwise, x ♡ y = y + y + x + 3 + x.\nand ○, the rules are as follows:\nwhen x is a multiple of 5, x ○ y = x * x - x - y;\notherwise, x ○ y = x - y * 5 * 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: 1 ○ 8 ⊕ 9 ♡ 8\nPlease fill your final answer in \\boxed{}."
},
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"simplified_expr": "( (( 1 - 8 * 5 * 2)) - (( 1 - 8 * 5 * 2)) - (( 9 + (3 * 3) - 8 * 3)) ** (( 9 + (3 * 3) - 8 * 3)) * (( 9 + (3 * 3) - 8 * 3)))",
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],
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],
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"seed": 197481,
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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和y的和是奇数时，x ⊕ y = x + y - x + x - (y)；
其他情况下，x ⊕ y = 5 + x / 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 / 4 ⊕ 3 ** 1 ♡ 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。\n和 ⊕，规则如下：\n当x和y的和是奇数时，x ⊕ y = x + y - x + x - (y)；\n其他情况下，x ⊕ y = 5 + x / 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 / 4 ⊕ 3 ** 1 ♡ 3\n请将最终答案填入\\boxed{}中。"
},
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},
"seed": 93292407,
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"task_type": "operation"
} |
logic-v2 | Define ○, the rules are as follows:
when x is a multiple of 5, x ○ y = y + 1 + 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: 5 ○ 3
Please fill your final answer in \boxed{}. | {
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},
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"question": "Define ○, the rules are as follows:\nwhen x is a multiple of 5, x ○ y = y + 1 + x;\notherwise, x ○ y = y + x + y.\nThe precedence of operations: ○ > ** > * = / = % > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 5 ○ 3\nPlease fill your final answer in \\boxed{}."
},
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"△": null,
"▽": null,
"◇": null,
"○": {
"associativity": "left",
"conditions": [
{
"condition": "x是5的倍数",
"operation": " y + 1 + x"
}
],
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},
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
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"trace_id": "40b0f713-6e2b-49e6-a27c-fb929b1587d7"
},
"seed": 28768888,
"task_id": 228768888,
"task_type": "operation"
} |
logic-v2 | Define ⊗, the rules are as follows:
on the real number field, x ⊗ y = abs(x) - y - x ** y.
and ⊙, the rules are as follows:
when x and y are both odd, x ⊙ y = x + y ** y - 4;
otherwise, x ⊙ y = (x / y - y).
and ◎, the rules are as follows:
on the real number field, 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: 8 ◎ 1 ⊙ 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 = abs(x) - y - x ** y.\nand ⊙, the rules are as follows:\nwhen x and y are both odd, x ⊙ y = x + y ** y - 4;\notherwise, x ⊙ y = (x / y - y).\nand ◎, the rules are as follows:\non the real number field, 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: 8 ◎ 1 ⊙ 9 ⊗ 4\nPlease fill your final answer in \\boxed{}."
},
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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 - y + x * x；
其他情况下，x ⊗ y = y + 5 * y * x / y。
和 ⊙，规则如下：
实数域上，x ⊙ y = y - x - x。
和 ♢，规则如下：
当y是5的倍数时，x ♢ y = 4 ⊗ y + x + y + x；
其他情况下，x ♢ y = x ⊗ 4 + 2 * 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: 1 ⊙ 3 ♢ 10
请将最终答案填入\boxed{}中。 | {
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"♢": {
"associativity": "left",
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"condition": "y是5的倍数",
"operation": " 4 ⊗ y + x + y + x"
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"question": "定义 ⊗，规则如下：\n当x和y的和是奇数时，x ⊗ y = x + y - y + x * x；\n其他情况下，x ⊗ y = y + 5 * y * x / y。\n和 ⊙，规则如下：\n实数域上，x ⊙ y = y - x - x。\n和 ♢，规则如下：\n当y是5的倍数时，x ♢ y = 4 ⊗ y + x + y + x；\n其他情况下，x ♢ y = x ⊗ 4 + 2 * 2 - 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 ♢ 10\n请将最终答案填入\\boxed{}中。"
},
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"operation": " 4 ⊗ y + x + y + x"
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],
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},
"seed": 5547072,
"task_id": 205547072,
"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 even, x ⊕ y = x ☆ x - x + y;
otherwise, x ⊕ y = 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: 5 ☆ 4
Please fill your final answer in \boxed{}. | {
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"default_operation": " x * y + y",
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"♢": null
},
"target": null,
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"trace_id": "c71e5793-ae00-41f6-8963-19f3378099d3"
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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 even, x ⊕ y = x ☆ x - x + y;\notherwise, x ⊕ y = 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: 5 ☆ 4\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
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"fill_length": null,
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"operators": null,
"question_sequence": null,
"seed": 43127716,
"simplified_expr": "( 5 * 4 + 4)",
"solutions_count": null,
"symbol_definitions": {
"⊕": {
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"conditions": [
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"condition": "x和y的和是偶数",
"operation": " x ☆ x - x + y"
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],
"default_operation": " y + x ** y / y",
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"☆": {
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"conditions": [],
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"precedence": 2
},
"♡": null,
"♢": null
},
"target": null,
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},
"seed": 43127716,
"task_id": 243127716,
"task_type": "operation"
} |
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: 7 + 10 ▽ 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 = 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 ▽ 1\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
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"default_operation": " x / x + y",
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logic-v2 | 定义 ♡，规则如下：
当x是偶数时，x ♡ y = x / y；
其他情况下，x ♡ y = x + y - y。
和 ☆，规则如下：
实数域上，x ☆ y = x + y - 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: 9 ♡ 9 ☆ 3
请将最终答案填入\boxed{}中。 | {
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"default_operation": " x + y - y",
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"♢": null
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"question": "定义 ♡，规则如下：\n当x是偶数时，x ♡ y = x / y；\n其他情况下，x ♡ y = x + y - y。\n和 ☆，规则如下：\n实数域上，x ☆ y = x + y - abs(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 ☆ 3\n请将最终答案填入\\boxed{}中。"
},
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"♡": {
"associativity": "left",
"conditions": [
{
"condition": "x是偶数",
"operation": " x / y"
}
],
"default_operation": " x + y - y",
"precedence": 3
},
"♢": null
},
"target": null,
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"trace_id": "c65963e2-ad10-4a14-ba26-ad251b874a3d"
},
"seed": 40965405,
"task_id": 240965405,
"task_type": "operation"
} |
logic-v2 | Define △, the rules are as follows:
when x and y are both odd, x △ y = x * x * y + x + x;
otherwise, x △ y = 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: 7 △ 1 % 8 * 1
Please fill your final answer in \boxed{}. | {
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"answer": "7",
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"operation": " x * x * y + x + x"
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"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
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"question": "Define △, the rules are as follows:\nwhen x and y are both odd, x △ y = x * x * y + x + x;\notherwise, x △ y = 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: 7 △ 1 % 8 * 1\nPlease fill your final answer in \\boxed{}."
},
"metadata": {
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"expression": "7 △ 1 % 8 * 1",
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"simplified_expr": "((((( 7 * 7 * 1 + 7 + 7)) % 8)) * 1)",
"solutions_count": null,
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"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": {
"associativity": "left",
"conditions": [
{
"condition": "x和y都是奇数",
"operation": " x * x * y + x + x"
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],
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},
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
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"trace_id": "8948cdc5-5f28-442b-a2c1-cb3a9c99a9ba"
},
"seed": 52950133,
"task_id": 252950133,
"task_type": "operation"
} |
logic-v2 | 定义 ◇，规则如下：
当y是3的倍数时，x ◇ y = y - (x * y - y) * 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: 2 ◇ 3 - 1
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 = x + y / x / y；
其他情况下，x △ y = (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: 4 ** 1 △ 3
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logic-v2 | 定义 ⊙，规则如下：
当x是偶数时，x ⊙ y = y + y - x；
其他情况下，x ⊙ y = x + x * y。
和 ○，规则如下：
当y是3的倍数时，x ○ y = (x ⊙ y) + 2 - y；
其他情况下，x ○ y = (x * y ⊙ 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: 2 △ 7 ○ 7 ⊙ 1
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logic-v2 | 定义 ⊗，规则如下：
当x是奇数时，x ⊗ y = 1 + x * y；
其他情况下，x ⊗ y = (y - 3) * x。
和 ⊕，规则如下：
当x小于y时，x ⊕ y = abs(y - y) - x；
其他情况下，x ⊕ y = x * 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 = 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: 2 ⊗ 7 ⊙ 4 ⊕ 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 - x / 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 = 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: 1 ○ 5 ◇ 9 ⊙ 1
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 + 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 △ 1
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 - y / x)；
其他情况下，x ♡ y = 1 + y + x。
和 ☆，规则如下：
实数域上，x ☆ y = x - x * y。
运算优先级：♡ > ☆ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ♡ 7 ☆ 4 ** 1 * 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的和是偶数时，x ◎ y = x - (y * y) * x；
其他情况下，x ◎ y = y - 4 + x - 4 - 2。
和 ⊗，规则如下：
实数域上，x ⊗ y = y * 2 + 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 + 6 / 8 ⊗ 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 = y * y - y + x.
and □, the rules are as follows:
when the sum of x and y is even, x □ y = y ** x + 2 ** 3 + 5;
otherwise, x □ y = x + y * x - y.
The precedence of operations: ** = ⊙ = □ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 2 □ 6 ⊙ 4
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 + 1 + x)。
和 ▽，规则如下：
实数域上，x ▽ y = y ◎ y - x。
运算优先级：◎ = ▽ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 ◎ 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 * x + y。
和 △，规则如下：
当x等于y时，x △ y = x - y / y / x ⊗ y；
其他情况下，x △ y = y - y ⊗ x - x * x。
和 □，规则如下：
实数域上，x □ y = x / 5 ⊗ 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: 2 ⊗ 8 △ 3 □ 6
请将最终答案填入\boxed{}中。 | {
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logic-v2 | 定义 ▽，规则如下：
实数域上，x ▽ y = (y + x) + x。
运算优先级：▽ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 ▽ 2 ▽ 1
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 odd, x ○ y = y * y - x;
otherwise, x ○ y = x + x + 2 - y.
and ◇, the rules are as follows:
when y is odd, x ◇ y = x * x / (x) + y;
otherwise, x ◇ y = y * x + 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: 2 ◇ 4 ○ 8
Please fill your final answer in \boxed{}. | {
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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；
其他情况下，x △ y = y - y + x。
和 ♡，规则如下：
当x和y的和是偶数时，x ♡ y = x * y △ 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 △ 5 ♡ 3 ** 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 = x * y + y - y。
和 △，规则如下：
实数域上，x △ y = x - x / x ** y。
和 ◎，规则如下：
当x是3的倍数时，x ◎ y = y * y - x - x；
其他情况下，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: 7 △ 1 ♢ 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 = abs(y * x)。
和 ♢，规则如下：
实数域上，x ♢ y = x ♡ y * (1 - y)。
和 △，规则如下：
当x是5的倍数时，x △ y = x ♢ y - (1 + 5)；
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: 3 ♡ 1 △ 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 = y / y / x.
and ▽, the rules are as follows:
on the real number field, x ▽ y = x ♢ y.
and ⊗, the rules are as follows:
when y is even, x ⊗ y = x + y;
otherwise, x ⊗ 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 ▽ 4 ▽ 6 ♢ 7 ⊗ 9
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 = 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 ▽ 1 + 9
Please fill your final answer in \boxed{}. | {
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logic-v2 | 定义 ▽，规则如下：
当x和y都是偶数时，x ▽ y = (y + x) * x；
其他情况下，x ▽ y = x + (y + y * y)。
运算优先级：** > * = / = % > + = - = ▽。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7 ▽ 6 ▽ 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 = x + y * x。
和 ▽，规则如下：
实数域上，x ▽ y = x * abs(y - y) - y。
和 △，规则如下：
实数域上，x △ y = x - 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: 7 △ 4 ▽ 2 - 6 ♢ 5
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 a multiple of 3, x ◇ y = 1 - y + x + x;
otherwise, x ◇ y = 1 + 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: 3
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 + 4 - 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: 5 ◇ 7 * 5
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。
和 ☆，规则如下：
当x大于y时，x ☆ y = abs(x - x) + y；
其他情况下，x ☆ y = x * y + 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: 8 □ 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y是奇数时，x ▽ y = 4 - y / x；
其他情况下，x ▽ y = x + y - y。
运算优先级：** > * = / = % = ▽ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 / 3 ▽ 8 ** 10
请将最终答案填入\boxed{}中。 | {
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"question": "定义 ▽，规则如下：\n当y是奇数时，x ▽ y = 4 - y / x；\n其他情况下，x ▽ y = x + y - y。\n运算优先级：** > * = / = % = ▽ > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 4 / 3 ▽ 8 ** 10\n请将最终答案填入\\boxed{}中。"
},
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logic-v2 | Define ◇, the rules are as follows:
on the real number field, x ◇ y = y - abs(x + x) / y.
and ⊕, the rules are as follows:
when x is less than y, x ⊕ y = y - y ◇ x;
otherwise, x ⊕ y = 4 * x * y ◇ 3.
and △, the rules are as follows:
on the real number field, x △ y = (y ** 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: 6 ◇ 2 ⊕ 8
Please fill your final answer in \boxed{}. | {
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"answer": "37.333333",
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},
"▽": null,
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"associativity": "left",
"conditions": [],
"default_operation": " y - abs(x + x) / y",
"precedence": 3
},
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": null
},
"target": null,
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"trace_id": "96199aa9-f3f0-47e3-8a99-7d26c09d8f9e"
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"question": "Define ◇, the rules are as follows:\non the real number field, x ◇ y = y - abs(x + x) / y.\nand ⊕, the rules are as follows:\nwhen x is less than y, x ⊕ y = y - y ◇ x;\notherwise, x ⊕ y = 4 * x * y ◇ 3.\nand △, the rules are as follows:\non the real number field, x △ y = (y ** x * 1).\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 ◇ 2 ⊕ 8\nPlease fill your final answer in \\boxed{}."
},
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"seed": 47336584,
"simplified_expr": "((((4 * ((2 - (((abs((6 + 6))) / 2)))))) * (( 3 - abs(8 + 8) / 3))))",
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"conditions": [],
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"♢": null
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"seed": 47336584,
"task_id": 247336584,
"task_type": "operation"
} |
logic-v2 | Define ☆, the rules are as follows:
on the real number field, x ☆ y = y + (y * y - x).
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = x + y ** 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: 10 ☆ 2
Please fill your final answer in \boxed{}. | {
"game_data": {
"answer": "-4",
"difficulty": 1,
"gpt_response": "",
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"simplified_expr": "( 2 + (2 * 2 - 10))",
"solutions_count": null,
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"▽": null,
"◇": null,
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"◎": null,
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"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "73e962c5-66c7-4e4f-9514-ad43950fdc3a"
},
"question": "Define ☆, the rules are as follows:\non the real number field, x ☆ y = y + (y * y - x).\nand ⊗, the rules are as follows:\non the real number field, x ⊗ y = x + y ** 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: 10 ☆ 2\nPlease fill your final answer in \\boxed{}."
},
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"□": null,
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": {
"associativity": "left",
"conditions": [],
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"♢": null
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},
"seed": 67750606,
"task_id": 267750606,
"task_type": "operation"
} |
logic-v2 | Define ♢, the rules are as follows:
on the real number field, x ♢ y = x * y - x.
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 greater than y, x ○ y = x + y;
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 □ 4 ○ 9 ♢ 2
Please fill your final answer in \boxed{}. | {
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"simplified_expr": "( (( 9 - (( 7 + 4 / 7)) - (( 7 + 4 / 7)))) * 2 - (( 9 - (( 7 + 4 / 7)) - (( 7 + 4 / 7)))))",
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"default_operation": " y - x - x",
"precedence": 5
},
"◎": null,
"☆": null,
"♡": null,
"♢": {
"associativity": "left",
"conditions": [],
"default_operation": " x * y - x",
"precedence": 1
}
},
"target": null,
"total_length": null,
"trace_id": "906d635e-907a-4dae-b145-1047dac83418"
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"question": "Define ♢, the rules are as follows:\non the real number field, x ♢ y = x * y - x.\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 greater than y, x ○ y = x + y;\notherwise, x ○ y = y - x - x.\nThe precedence of operations: □ = ○ > ** > * = / = % > + = - = ♢。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 7 □ 4 ○ 9 ♢ 2\nPlease fill your final answer in \\boxed{}."
},
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"expression": "7 □ 4 ○ 9 ♢ 2",
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"seed": 55172008,
"simplified_expr": "( (( 9 - (( 7 + 4 / 7)) - (( 7 + 4 / 7)))) * 2 - (( 9 - (( 7 + 4 / 7)) - (( 7 + 4 / 7)))))",
"solutions_count": null,
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],
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},
"◎": null,
"☆": null,
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"♢": {
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}
},
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},
"seed": 55172008,
"task_id": 255172008,
"task_type": "operation"
} |
logic-v2 | Define ◎, the rules are as follows:
on the real number field, x ◎ y = (y + y + x - x ** 1).
and ▽, the rules are as follows:
on the real number field, x ▽ y = 3 * 2 * 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: 4 ◎ 8
Please fill your final answer in \boxed{}. | {
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"symbol_definitions": {
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"○": null,
"◎": {
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"conditions": [],
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},
"☆": null,
"♡": null,
"♢": null
},
"target": null,
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"question": "Define ◎, the rules are as follows:\non the real number field, x ◎ y = (y + y + x - x ** 1).\nand ▽, the rules are as follows:\non the real number field, x ▽ y = 3 * 2 * 4 - 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 ◎ 8\nPlease fill your final answer in \\boxed{}."
},
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"default_operation": " 3 * 2 * 4 - x - y",
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"○": null,
"◎": {
"associativity": "left",
"conditions": [],
"default_operation": " (y + y + x - x ** 1)",
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"seed": 73583688,
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} |
logic-v2 | Define ☆, the rules are as follows:
on the real number field, x ☆ y = 1 - x + x / y - 1.
and ⊕, the rules are as follows:
on the real number field, x ⊕ y = x + y * 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: 3 ** 2 ☆ 4 ⊕ 9
Please fill your final answer in \boxed{}. | {
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"symbol_definitions": {
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"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": {
"associativity": "left",
"conditions": [],
"default_operation": " 1 - x + x / y - 1",
"precedence": 5
},
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "b3cb12a3-12d0-498c-a3c7-b47c6522b348"
},
"question": "Define ☆, the rules are as follows:\non the real number field, x ☆ y = 1 - x + x / y - 1.\nand ⊕, the rules are as follows:\non the real number field, x ⊕ y = x + y * 1.\nThe precedence of operations: ☆ = ⊕ > ** > * = / = % > + = -。\nParentheses have the highest priority, and the expression inside the parentheses is calculated first.\nPlease calculate the value of the expression: 3 ** 2 ☆ 4 ⊕ 9\nPlease fill your final answer in \\boxed{}."
},
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"seed": 14825054,
"simplified_expr": "(3 ** (( (( 1 - 2 + 2 / 4 - 1)) + 9 * 1)))",
"solutions_count": null,
"symbol_definitions": {
"⊕": {
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"precedence": 5
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"⊙": null,
"□": null,
"△": null,
"▽": null,
"◇": null,
"○": null,
"◎": null,
"☆": {
"associativity": "left",
"conditions": [],
"default_operation": " 1 - x + x / y - 1",
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"♢": null
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},
"seed": 14825054,
"task_id": 214825054,
"task_type": "operation"
} |
logic-v2 | Define ♢, the rules are as follows:
when the sum of x and y is even, x ♢ y = y + x * x;
otherwise, x ♢ y = x + y - 4.
and ▽, the rules are as follows:
when the sum of x and y is odd, x ▽ y = abs(y * x / x);
otherwise, x ▽ y = 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: 3 ▽ 1 ▽ 5 - 8 ♢ 8
Please fill your final answer in \boxed{}. | {
"game_data": {
"answer": "-70.285714",
"difficulty": 1,
"gpt_response": "",
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"expression": "3 ▽ 1 ▽ 5 - 8 ♢ 8",
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"numbers": null,
"operators": null,
"question_sequence": null,
"seed": 44419886,
"simplified_expr": "((((3 / (( 5 + ((3 / ((3 + ((1 * 1)))))) - 4))))) - (( 8 + 8 * 8)))",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": null,
"▽": {
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"operation": " abs(y * x / x)"
}
],
"default_operation": " 3 / (y ♢ x)",
"precedence": 3
},
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": null,
"♢": {
"associativity": "left",
"conditions": [
{
"condition": "x和y的和是偶数",
"operation": " y + x * x"
}
],
"default_operation": " x + y - 4",
"precedence": 3
}
},
"target": null,
"total_length": null,
"trace_id": "7a0a31ef-3588-4b40-b94f-38738ff9e0f6"
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"question": "Define ♢, the rules are as follows:\nwhen the sum of x and y is even, x ♢ y = y + x * x;\notherwise, x ♢ y = x + y - 4.\nand ▽, the rules are as follows:\nwhen the sum of x and y is odd, x ▽ y = abs(y * x / x);\notherwise, x ▽ y = 3 / (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: 3 ▽ 1 ▽ 5 - 8 ♢ 8\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 = 1 + 5 + 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: 5 ○ 3 % 7
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 = (y - y) - x；
其他情况下，x △ y = y + (x - x)。
和 ○，规则如下：
当y是3的倍数时，x ○ y = x + y * x；
其他情况下，x ○ y = x * y + 1。
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: 5 ☆ 10 - 6 △ 7 △ 10 ○ 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是偶数时，x ♢ y = x + abs(y + y)；
其他情况下，x ♢ y = x + y。
和 ◇，规则如下：
实数域上，x ◇ y = x * 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: 1 ⊙ 4 ◇ 1 ♢ 2
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 even, x △ y = y + x - y - y * x;
otherwise, x △ y = y + 2 ** x + y * x.
The precedence of operations: △ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 7 / 3 △ 1
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 + y * x / x * y。
和 ☆，规则如下：
当y是3的倍数时，x ☆ y = y / x + y - y + y；
其他情况下，x ☆ y = x / y ◎ 1 * 5。
和 ♡，规则如下：
实数域上，x ♡ 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: 2 ♡ 3 / 9 ♡ 10 ◎ 6 ☆ 2
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 = 1 + x + y / y。
运算优先级：** = ▽ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7 ▽ 2 + 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 = y + y + x.
and △, the rules are as follows:
on the real number field, x △ y = (y - x) * y.
and ▽, the rules are as follows:
when y is a multiple of 3, x ▽ y = (x + 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: 3 △ 6 ▽ 1 ⊕ 1 * 4
Please 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 = y * x + y * x + x；
其他情况下，x ⊙ y = y * x * x + y - x。
和 ◎，规则如下：
实数域上，x ◎ y = y - y ⊙ (3 - 2) * x。
和 ▽，规则如下：
实数域上，x ▽ y = y * (x + 4) - 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 ⊙ 8 ◎ 8
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3的倍数时，x ⊙ y = y * x + y * x + x；\n其他情况下，x ⊙ y = y * x * x + y - x。\n和 ◎，规则如下：\n实数域上，x ◎ y = y - y ⊙ (3 - 2) * x。\n和 ▽，规则如下：\n实数域上，x ▽ y = y * (x + 4) - 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 ⊙ 8 ◎ 8\n请将最终答案填入\\boxed{}中。"
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logic-v2 | 定义 ⊙，规则如下：
当x是偶数时，x ⊙ y = y * x；
其他情况下，x ⊙ y = x * x - y。
和 ○，规则如下：
当y是偶数时，x ○ y = 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 + 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 ⊙ 4 ○ 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是偶数时，x ⊙ y = y * x；\n其他情况下，x ⊙ y = x * x - y。\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 = y ⊙ x。\n和 ◇，规则如下：\n实数域上，x ◇ y = (y - x + x)。\n运算优先级：⊙ = ◇ > ** = ○ > * = / = % > + = -。\n括号具有最高优先级，先计算括号内的表达式。\n请计算表达式的值: 1 ⊙ 4 ○ 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 a multiple of 3, x ⊗ y = x * x * x - y;
otherwise, x ⊗ y = x + y ** 2 + y - x.
and ◎, the rules are as follows:
on the real number field, x ◎ y = y - x + x ** y ⊗ x.
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = (x + 4 + 2) + y / 2.
The precedence of operations: ◎ > ** > * = / = % = ⊗ = ⊙ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 3 ⊙ 5 ◎ 3 ⊗ 8 ⊙ 2
Please fill your final answer in \boxed{}. | {
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logic-v2 | 定义 ⊕，规则如下：
实数域上，x ⊕ y = x + y。
和 ▽，规则如下：
实数域上，x ▽ y = x * y。
和 ♡，规则如下：
当x和y的和是偶数时，x ♡ y = y ** x * y；
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: 2 ▽ 1 ♡ 8 ⊕ 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 + y。\n和 ▽，规则如下：\n实数域上，x ▽ y = x * y。\n和 ♡，规则如下：\n当x和y的和是偶数时，x ♡ y = y ** x * y；\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: 2 ▽ 1 ♡ 8 ⊕ 7\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
"closing_sequence": null,
"expression": "2 ▽ 1 ♡ 8 ⊕ 7",
"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": 72802405,
"simplified_expr": "( (( 8 ** (( 2 * 1)) * 8)) + 7)",
"solutions_count": null,
"symbol_definitions": {
"⊕": {
"associativity": "left",
"conditions": [],
"default_operation": " x + y",
"precedence": 2
},
"⊗": null,
"⊙": null,
"□": null,
"△": null,
"▽": {
"associativity": "left",
"conditions": [],
"default_operation": " x * y",
"precedence": 4
},
"◇": null,
"○": null,
"◎": null,
"☆": null,
"♡": {
"associativity": "left",
"conditions": [
{
"condition": "x和y的和是偶数",
"operation": " y ** x * y"
}
],
"default_operation": " y + y + x",
"precedence": 4
},
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "d6591e3c-dde3-4173-a87d-0b1224ef7e2f"
},
"seed": 72802405,
"task_id": 272802405,
"task_type": "operation"
} |
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 - 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 ◎ 10 △ 5 + 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-83",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ◎ 10 △ 5 + 7",
"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": 58233000,
"simplified_expr": "((( (( (10 - 10 - 10) * 5 + 5)) - 9 * 5)) + 7)",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": {
"associativity": "left",
"conditions": [],
"default_operation": " (x - x - x) * y + y",
"precedence": 4
},
"▽": null,
"◇": null,
"○": null,
"◎": {
"associativity": "left",
"conditions": [],
"default_operation": " y - x * 5",
"precedence": 1
},
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "57171415-ba7a-436d-a3a2-bf61ce651248"
},
"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 - 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 ◎ 10 △ 5 + 7\n请将最终答案填入\\boxed{}中。"
},
"metadata": {
"closing_sequence": null,
"expression": "9 ◎ 10 △ 5 + 7",
"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": 58233000,
"simplified_expr": "((( (( (10 - 10 - 10) * 5 + 5)) - 9 * 5)) + 7)",
"solutions_count": null,
"symbol_definitions": {
"⊕": null,
"⊗": null,
"⊙": null,
"□": null,
"△": {
"associativity": "left",
"conditions": [],
"default_operation": " (x - x - x) * y + y",
"precedence": 4
},
"▽": null,
"◇": null,
"○": null,
"◎": {
"associativity": "left",
"conditions": [],
"default_operation": " y - x * 5",
"precedence": 1
},
"☆": null,
"♡": null,
"♢": null
},
"target": null,
"total_length": null,
"trace_id": "57171415-ba7a-436d-a3a2-bf61ce651248"
},
"seed": 58233000,
"task_id": 258233000,
"task_type": "operation"
} |
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