env stringclasses 1
value | prompt stringlengths 119 673 | extra dict |
|---|---|---|
logic-v2 | Define ♡, the rules are as follows:
when y is even, x ♡ y = 2 * y * (x);
otherwise, 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:
on the real number field, x ◎ y = y * y * x.
The precedence of operations: ♡ = ◎ > ** = △ > * = ... | {
"game_data": {
"answer": "-35",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ◎ 2 ♡ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_de... |
logic-v2 | 定义 ◇，规则如下：
当x等于y时，x ◇ y = x + y ** x * 2；
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 - 6 ◇ 10 % 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "10",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 - 6 ◇ 10 % 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesti... |
logic-v2 | Define ⊗, the rules are as follows:
on the real number field, x ⊗ y = y + (x * x).
and ♢, the rules are as follows:
when x is a multiple of 5, x ♢ y = x * x / y;
otherwise, x ♢ y = (x / 3 / y).
and △, the rules are as follows:
when x is less than y, x △ y = abs(x - y) - y;
otherwise, x △ y = (y - x) ♢ x.
The ... | {
"game_data": {
"answer": "-0.270869",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ⊗ 2 ♢ 3 ♢ 8 △ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
... |
logic-v2 | Define △, the rules are as follows:
when x and y are both odd, x △ y = 4 - (y * 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 th... | {
"game_data": {
"answer": "9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 - 3 △ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dep... |
logic-v2 | Define ⊙, the rules are as follows:
on the real number field, x ⊙ y = x + (3 * 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 ⊙ y / x.
The precedence of operations: ⊙ > ** = ○ = ♢ > * = / = % > + = -。
Parenth... | {
"game_data": {
"answer": "-12",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ♢ 7 + 10 ⊙ 2 ○ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"n... |
logic-v2 | 定义 ▽，规则如下：
当x是5的倍数时，x ▽ y = x - y * y - y ** x；
其他情况下，x ▽ y = 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: 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | Define ▽, the rules are as follows:
when y is even, x ▽ y = abs(y + 4) * 5 + x;
otherwise, x ▽ y = abs(x / x * y).
The precedence of operations: ▽ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the express... | {
"game_data": {
"answer": "165",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ▽ 2 * 2 ▽ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nestin... |
logic-v2 | Define ☆, 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
Please fill your final answer... | {
"game_data": {
"answer": "6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null... |
logic-v2 | 定义 ◎，规则如下：
实数域上，x ◎ y = x + y * y / x / x。
和 ♡，规则如下：
实数域上，x ♡ y = x + x ◎ y。
运算优先级：♡ > ** > * = / = % = ◎ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 ♡ 3 ◎ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "16.236587",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ♡ 3 ◎ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nest... |
logic-v2 | 定义 ⊕，规则如下：
实数域上，x ⊕ y = y + x / 2 + 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 = y * y * x + x。
和 ◇，规则如下：
当y是奇数时，x ◇ y = 4 + 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: 1 ⊙ 4 ⊕ 4 ◇ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "879.25",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ⊙ 4 ⊕ 4 ◇ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nes... |
logic-v2 | 定义 ☆，规则如下：
实数域上，x ☆ y = (y) * x。
和 ▽，规则如下：
实数域上，x ▽ y = x ☆ y * x + 3。
运算优先级：▽ > ** = ☆ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 / 5 ▽ 1 ☆ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0.020408",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 / 5 ▽ 1 ☆ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"n... |
logic-v2 | 定义 △，规则如下：
当y是偶数时，x △ y = x + abs(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: 7 △ 4 △ 9 / 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "10",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 △ 4 △ 9 / 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting... |
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 = y * x - y - 4。
和 ⊙，规则如下：
实数域上，x ⊙ y = abs(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 ☆ 2 ⊙ 10 * 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "20000",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ☆ 2 ⊙ 10 * 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nes... |
logic-v2 | Define ◇, the rules are as follows:
on the real number field, x ◇ y = x * y - abs(x) * 5.
The precedence of operations: ◇ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 9 ◇ 9 - 1
Please fill ... | {
"game_data": {
"answer": "35",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ◇ 9 - 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dep... |
logic-v2 | 定义 ☆，规则如下：
当y是3的倍数时，x ☆ y = x + y；
其他情况下，x ☆ y = x + x + y。
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: 10 ♡ 7 ☆ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "425",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ♡ 7 ☆ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_d... |
logic-v2 | Define □, the rules are as follows:
on the real number field, x □ y = 3 + y + x * 1.
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 calcula... | {
"game_data": {
"answer": "33",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 □ 9 ⊗ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dep... |
logic-v2 | Define ◇, the rules are as follows:
on the real number field, x ◇ y = x - y - 5 - x.
The precedence of operations: ◇ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 9 - 10 ◇ 8
Please fill your... | {
"game_data": {
"answer": "22",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 - 10 ◇ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_de... |
logic-v2 | 定义 ☆，规则如下：
实数域上，x ☆ y = (y / 3 - 3) + x。
和 △，规则如下：
实数域上，x △ y = x * 5 * (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 △ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "25",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 △ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth":... |
logic-v2 | 定义 △，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: 3 △ 8 △ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "75",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 △ 8 △ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dep... |
logic-v2 | Define ▽, the rules are as follows:
when x and y are both odd, x ▽ y = 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: ... | {
"game_data": {
"answer": "12",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ▽ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth":... |
logic-v2 | Define ◎, the rules are as follows:
on the real number field, x ◎ y = 1 * y * x.
and ⊙, the rules are as follows:
when x is greater than y, x ⊙ y = y + x + y ◎ 1;
otherwise, x ⊙ y = y - x - x * x.
The precedence of operations: ⊙ > ** > * = / = % > + = - = ◎。
Parentheses have the highest priority, and the expressi... | {
"game_data": {
"answer": "42",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ◎ 1 ⊙ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dep... |
logic-v2 | 定义 ◎，规则如下：
实数域上，x ◎ y = y - 1 / x + y。
和 ◇，规则如下：
当x等于y时，x ◇ y = y / (y) + x；
其他情况下，x ◇ y = y * x - x / x。
运算优先级：◇ > ** > * = / = % > + = - = ◎。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 ◇ 7 ◎ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "15.985507",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ◇ 7 ◎ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nes... |
logic-v2 | 定义 ◇，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: 9 ◇ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-63",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ◇ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth"... |
logic-v2 | 定义 ♢，规则如下：
当y是5的倍数时，x ♢ y = (x * x) + x + y；
其他情况下，x ♢ y = y * y + y - x + y。
和 ⊕，规则如下：
实数域上，x ⊕ y = 2 - x * y - x。
和 ◇，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: 4 ♢ 3 ⊕ 1 ◇ 8 ◇ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-18.625",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ♢ 3 ⊕ 1 ◇ 8 ◇ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
... |
logic-v2 | Define △, the rules are as follows:
when the sum of x and y is odd, x △ y = 1 * x + y + 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... | {
"game_data": {
"answer": "738",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ** 3 △ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_d... |
logic-v2 | 定义 ○，规则如下：
当x和y都是偶数时，x ○ y = y * x + y + 5；
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: 5 - 7 ○ 1 / 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "3.714286",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 - 7 ○ 1 / 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"n... |
logic-v2 | Define △, the rules are as follows:
when x is a multiple of 5, x △ y = x - x - y / 1;
otherwise, x △ y = 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 expre... | {
"game_data": {
"answer": "16",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 △ 8 △ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dep... |
logic-v2 | 定义 ⊗，规则如下：
当y是5的倍数时，x ⊗ y = 4 * x * 4 - x - y；
其他情况下，x ⊗ y = x * y + y * x。
和 ☆，规则如下：
实数域上，x ☆ y = x + 3 ⊗ 3 / x * y。
和 △，规则如下：
当x是偶数时，x △ y = x * y + x + x + y；
其他情况下，x △ y = y * abs(x + 5 - 2) + y。
运算优先级：** = ☆ > * = / = % = △ > + = - = ⊗。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 ☆ 3 ⊗ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "216",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ☆ 3 ⊗ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_de... |
logic-v2 | 定义 △，规则如下：
当y是奇数时，x △ y = y / y - 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: 6 % 10 △ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-83",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 % 10 △ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_d... |
logic-v2 | Define ○, the rules are as follows:
when x and y are both even, x ○ y = y - x / x * x * y;
otherwise, 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 expre... | {
"game_data": {
"answer": "-168",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ○ 6 * 2 * 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesti... |
logic-v2 | 定义 ⊙，规则如下：
当x和y都是偶数时，x ⊙ y = x ** y - (x)；
其他情况下，x ⊙ y = y + abs(x)。
和 ♢，规则如下：
实数域上，x ♢ y = y ⊙ (x + 2)。
和 △，规则如下：
实数域上，x △ y = x - y + 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 ⊙ 4 ♢ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "13",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 △ 2 ⊙ 4 ♢ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nestin... |
logic-v2 | 定义 ♡，规则如下：
实数域上，x ♡ y = y * x - (y) * y。
和 ○，规则如下：
实数域上，x ○ y = x + 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: 7 ○ 6 ♡ 4 * 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1372",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ○ 6 ♡ 4 * 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesti... |
logic-v2 | Define △, the rules are as follows:
when the sum of x and y is even, x △ y = y * y + x + y;
otherwise, x △ y = x * y / y.
The precedence of operations: ** = △ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the ... | {
"game_data": {
"answer": "9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null... |
logic-v2 | Define ◇, the rules are as follows:
on the real number field, x ◇ y = x * (y) + y.
The precedence of operations: ◇ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 3 ◇ 1
Please fill your final ... | {
"game_data": {
"answer": "4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ◇ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": ... |
logic-v2 | Define □, the rules are as follows:
when x and y are both odd, x □ y = y + (y * x);
otherwise, x □ y = 4 / x + y.
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 in... | {
"game_data": {
"answer": "1.4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 △ 4 □ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_de... |
logic-v2 | Define ◇, the rules are as follows:
when x is greater than y, x ◇ y = y ** x;
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 ... | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 % 1 ◇ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dept... |
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: 6 ▽ 2
Please fill your fina... | {
"game_data": {
"answer": "-8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ▽ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth":... |
logic-v2 | Define ▽, the rules are as follows:
on the real number field, x ▽ y = y ** y / x ** 2.
The precedence of operations: ** = ▽ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 5 ▽ 4 ▽ 6 / 3
Please fill... | {
"game_data": {
"answer": "148.31543",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ▽ 4 ▽ 6 / 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"... |
logic-v2 | 定义 □，规则如下：
当x是5的倍数时，x □ y = abs(3 / x + y - 1) - x；
其他情况下，x □ y = 2 * y - 1 * 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: 3 ◇ 10 ◇ 10 ◇ 8 □ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "279",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ◇ 10 ◇ 10 ◇ 8 □ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"... |
logic-v2 | Define ⊕, the rules are as follows:
on the real number field, x ⊕ y = 2 + x - x + y.
and □, the rules are as follows:
when x is greater than y, x □ y = y * x ⊕ x;
otherwise, x □ y = (x - y) - x * 5.
and ♡, the rules are as follows:
on the real number field, x ♡ y = y □ x / x - 2.
The precedence of operations: ♡... | {
"game_data": {
"answer": "85",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ♡ 5 □ 2 ⊕ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting... |
logic-v2 | Define ◇, the rules are as follows:
when y is odd, x ◇ y = y + x * y;
otherwise, x ◇ y = x - y + x.
and ⊗, the rules are as follows:
when x is less than y, x ⊗ y = x ◇ y;
otherwise, x ⊗ y = (x + y) * x.
and ⊕, the rules are as follows:
when the sum of x and y is odd, x ⊕ y = y + x;
otherwise, x ⊕ y = x - (y... | {
"game_data": {
"answer": "0.0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ⊗ 7 ⊕ 10 ** 2 ◇ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"... |
logic-v2 | Define ▽, the rules are as follows:
when x and y are both odd, x ▽ y = (x) * y + x + y;
otherwise, x ▽ y = x * y + x * x - 3.
The precedence of operations: ▽ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of ... | {
"game_data": {
"answer": "59",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ▽ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth":... |
logic-v2 | Define □, the rules are as follows:
on the real number field, x □ y = y + y + x / x.
and ◇, the rules are as follows:
on the real number field, x ◇ y = y / abs(y / x) * x.
The precedence of operations: □ > ** = ◇ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses i... | {
"game_data": {
"answer": "81",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 □ 4 ◇ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dep... |
logic-v2 | 定义 ⊕，规则如下：
实数域上，x ⊕ y = abs(y - y + x)。
和 □，规则如下：
当x大于y时，x □ y = 5 * x * y；
其他情况下，x □ y = y - abs(4 ** x - y)。
和 ⊗，规则如下：
当x和y的和是偶数时，x ⊗ y = (x * y ** 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: 8 □ 7 ⊗ 1 ⊕ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 □ 7 ⊗ 1 ⊕ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_... |
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 + x。
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 ♢ 3 ⊙ 8 ◇ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1200",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ♢ 3 ⊙ 8 ◇ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesti... |
logic-v2 | 定义 ⊗，规则如下：
当y是奇数时，x ⊗ y = 1 - y + x + x + x；
其他情况下，x ⊗ y = x * x - y + y。
和 ♢，规则如下：
当x是3的倍数时，x ♢ y = y + x / x + x；
其他情况下，x ♢ y = y + x / y * x。
和 ▽，规则如下：
实数域上，x ▽ y = x * 3 ♢ 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: 6 ⊗ 8 ▽ 9 ♢ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "435",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ⊗ 8 ▽ 9 ♢ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nestin... |
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 = y - x + 4 - x.
The precedence of operations: ☆ > ** = ▽ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated ... | {
"game_data": {
"answer": "4.99514",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ☆ 10 ** 5 ▽ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"... |
logic-v2 | 定义 ♡，规则如下：
当x大于y时，x ♡ y = abs(x - x) + y * x；
其他情况下，x ♡ y = y + x * y * 3。
和 ⊕，规则如下：
当x是5的倍数时，x ⊕ y = 4 * y / x；
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: 5 ♡ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "112",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ♡ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth"... |
logic-v2 | Define □, the rules are as follows:
when x is greater than y, x □ y = x * x * 5 / x + y;
otherwise, x □ y = 1 - x + 4 - 1 * y.
and △, the rules are as follows:
on the real number field, x △ y = x - x + y - 4 □ x.
The precedence of operations: ** > * = / = % = △ > + = - = □。
Parentheses have the highest priority, ... | {
"game_data": {
"answer": "5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 △ 7 □ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dept... |
logic-v2 | 定义 ♢，规则如下：
当x是奇数时，x ♢ y = 3 * (x / y)；
其他情况下，x ♢ y = x - y + x。
和 ▽，规则如下：
当x是3的倍数时，x ▽ y = (x ** y)；
其他情况下，x ▽ y = x + y。
和 ⊙，规则如下：
实数域上，x ⊙ y = x - y - x。
运算优先级：▽ > ** = ♢ > * = / = % > + = - = ⊙。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 ♢ 10 ▽ 5 ⊙ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ♢ 10 ▽ 5 ⊙ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nestin... |
logic-v2 | Define ♡, the rules are as follows:
on the real number field, x ♡ y = abs(x + y - 1) / y - 1.
and □, the rules are as follows:
on the real number field, x □ y = (x - x ** y ** x * y).
The precedence of operations: □ > ** = ♡ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the p... | {
"game_data": {
"answer": "-2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ♡ 9 □ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dep... |
logic-v2 | 定义 △，规则如下：
当x等于y时，x △ y = y / x；
其他情况下，x △ y = x * y + y。
运算优先级：** > * = / = % = △ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 9 △ 9 ** 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "65610",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 △ 9 ** 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting... |
logic-v2 | 定义 ◇，规则如下：
当x小于y时，x ◇ y = (y / x)；
其他情况下，x ◇ y = y * abs(x)。
运算优先级：** > * = / = % = ◇ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 / 4 % 1 ◇ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 / 4 % 1 ◇ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_... |
logic-v2 | 定义 △，规则如下：
实数域上，x △ y = 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 △ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "34",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 △ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth":... |
logic-v2 | 定义 ◎，规则如下：
实数域上，x ◎ y = y + x * abs(x + x)。
和 ☆，规则如下：
实数域上，x ☆ y = (x + x * y) * y。
运算优先级：** > * = / = % > + = - = ◎ = ☆。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 ◎ 1 ☆ 3 * 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "3078",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ◎ 1 ☆ 3 * 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesti... |
logic-v2 | Define □, the rules are as follows:
on the real number field, x □ y = x + y * x * y * y.
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 cal... | {
"game_data": {
"answer": "845",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ⊗ 2 □ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_de... |
logic-v2 | Define △, the rules are as follows:
on the real number field, x △ y = x - x * x + y.
The precedence of operations: △ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 1 △ 2
Please fill your fina... | {
"game_data": {
"answer": "2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 △ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": ... |
logic-v2 | Define △, the rules are as follows:
when x and y are both even, x △ y = (y / y - y - 1 * x);
otherwise, x △ y = x / y - y + x.
The precedence of operations: ** = △ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of... | {
"game_data": {
"answer": "5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null... |
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3的倍数时，x ⊙ y = y * 3 - x；
其他情况下，x ⊙ y = (x - 3 / x) + y ☆ y。
运算优先级：☆ = ⊙ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5 * 7 ⊙ 4 * 6 ☆ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-128.571429",
"difficulty": 1,
"gpt_response": "",
"metadata": {
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"expression": "5 * 7 ⊙ 4 * 6 ☆ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
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"n_types": null,
... |
logic-v2 | 定义 ⊗，规则如下：
当y是奇数时，x ⊗ y = x + y + x * x；
其他情况下，x ⊗ y = x + y。
和 □，规则如下：
实数域上，x □ y = x * x + y * x。
和 ♡，规则如下：
当x是3的倍数时，x ♡ y = x - x - x □ 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: 6 □ 8 ♡ 3 ⊗ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-7302",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 □ 8 ♡ 3 ⊗ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nest... |
logic-v2 | Define ♢, the rules are as follows:
when x and y are both odd, x ♢ y = y * x + x;
otherwise, x ♢ y = abs(x + y * y).
and ♡, the rules are as follows:
when x is less than y, x ♡ y = x + y - y;
otherwise, x ♡ y = x - y * 2.
and ▽, the rules are as follows:
when y is a multiple of 3, x ▽ y = y * x - y;
otherwise... | {
"game_data": {
"answer": "8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ♢ 10 ♡ 7 ▽ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting... |
logic-v2 | Define ⊗, the rules are as follows:
when x and y are both odd, x ⊗ y = y - x - y;
otherwise, x ⊗ y = y - (y + x).
and □, the rules are as follows:
when x is odd, x □ y = abs(x) + y / x;
otherwise, x □ y = x ⊗ x * y.
and ♢, the rules are as follows:
when y is odd, x ♢ y = y - x + abs(x);
otherwise, x ♢ y = y... | {
"game_data": {
"answer": "20",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 □ 5 ⊗ 4 ♢ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting... |
logic-v2 | Define ⊙, the rules are as follows:
on the real number field, x ⊙ y = x * x - x * y.
and ♢, the rules are as follows:
on the real number field, x ♢ y = x * x + y.
and ▽, the rules are as follows:
on the real number field, x ▽ y = y * x * y + 3.
The precedence of operations: ▽ > ** > * = / = % = ⊙ = ♢ > + = -。
Par... | {
"game_data": {
"answer": "49932",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ▽ 5 ⊙ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_... |
logic-v2 | 定义 ○，规则如下：
实数域上，x ○ y = 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: 8 * 5 ○ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "136",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 * 5 ○ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_de... |
logic-v2 | 定义 ☆，规则如下：
当x是3的倍数时，x ☆ y = (y / x * x)；
其他情况下，x ☆ y = y + 1 ** 3 * x + y。
和 ◇，规则如下：
当x和y都是奇数时，x ◇ y = abs(x / y) * y + x；
其他情况下，x ◇ y = x ** y + y。
运算优先级：◇ > ** > * = / = % = ☆ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 9 * 3 ◇ 4 ☆ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "2.0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 * 3 ◇ 4 ☆ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nestin... |
logic-v2 | 定义 ♡，规则如下：
当x和y都是偶数时，x ♡ y = y + 2 + x；
其他情况下，x ♡ y = y - abs(y) * x。
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 ♡ 5 ☆ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ♡ 5 ☆ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dept... |
logic-v2 | Define ⊕, the rules are as follows:
when y is a multiple of 3, x ⊕ y = (x + y * 5 / x);
otherwise, x ⊕ y = y - y / x / y.
and ♢, the rules are as follows:
when x and y are both odd, x ♢ y = y + y ⊕ x + y;
otherwise, x ♢ y = y + x * x.
and ♡, the rules are as follows:
on the real number field, x ♡ y = (4 + x ⊕... | {
"game_data": {
"answer": "-100.008503",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 - 7 ♢ 5 ⊕ 9 * 7 ♡ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": nul... |
logic-v2 | Define ♡, the rules are as follows:
when x is less than y, x ♡ y = x / y + (x + x * x);
otherwise, x ♡ y = x + y * x - x * y.
and ◎, the rules are as follows:
on the real number field, x ◎ y = y - y - x + x - x.
and ○, the rules are as follows:
when x and y are both odd, x ○ y = y - (x - x ** x * x);
otherwise,... | {
"game_data": {
"answer": "2.5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ○ 8 ○ 1 ♡ 2 ◎ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"ne... |
logic-v2 | 定义 ♢，规则如下：
实数域上，x ♢ y = abs(y + x - x)。
和 ♡，规则如下：
实数域上，x ♡ y = abs(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: 4 ♡ 1 / 9 ♡ 1 ⊙ 6 ♢ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "8.0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ♡ 1 / 9 ♡ 1 ⊙ 6 ♢ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
... |
logic-v2 | Define △, the rules are as follows:
when y is a multiple of 3, x △ y = x - y - y * y;
otherwise, 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 ex... | {
"game_data": {
"answer": "3",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null... |
logic-v2 | Define ◇, the rules are as follows:
when x and y are both odd, x ◇ y = x - y + 1 + y - 5;
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 th... | {
"game_data": {
"answer": "10000",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ◇ 9 ** 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nestin... |
logic-v2 | 定义 ♢，规则如下：
实数域上，x ♢ y = x + y + x * y。
和 △，规则如下：
当x和y都是奇数时，x △ y = x ♢ x / y + (y)；
其他情况下，x △ y = x + y - x。
和 ⊕，规则如下：
实数域上，x ⊕ y = 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: 3 + 6 ⊕ 10 ♢ 8 △ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "29604",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 + 6 ⊕ 10 ♢ 8 △ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
... |
logic-v2 | 定义 ◎，规则如下：
实数域上，x ◎ y = 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: 8 ◎ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "80",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ◎ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth"... |
logic-v2 | Define ⊗, the rules are as follows:
when x is greater than y, x ⊗ y = x * 5 * y * x;
otherwise, x ⊗ y = y + x * (y + x).
and ♡, the rules are as follows:
on the real number field, x ♡ y = y / 2 ⊗ x - x.
and ♢, the rules are as follows:
when x is a multiple of 3, x ♢ y = y ** x ⊗ y;
otherwise, x ♢ y = x - y * ... | {
"game_data": {
"answer": "-18496.75",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ♡ 5 ♢ 8 ⊗ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"... |
logic-v2 | Define ◇, the rules are as follows:
when x is even, x ◇ y = x + y + y + x;
otherwise, x ◇ y = 5 * 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: 3... | {
"game_data": {
"answer": "25",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 % 5 + 2 ◇ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting... |
logic-v2 | 定义 ⊗，规则如下：
当x和y的和是偶数时，x ⊗ y = x + y + y + y；
其他情况下，x ⊗ y = x + 2 * y + x。
和 ♢，规则如下：
当x等于y时，x ♢ y = x - x * y；
其他情况下，x ♢ y = 5 ⊗ 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
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "22",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ♢ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth":... |
logic-v2 | 定义 □，规则如下：
当x和y都是奇数时，x □ y = x + y + x + (x - x)；
其他情况下，x □ y = x - (3) + y + x。
和 ⊕，规则如下：
当x和y都是偶数时，x ⊕ y = x / 5 / y * y + x；
其他情况下，x ⊕ y = (x - x □ 1 - 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: 2 □ 8 ⊕ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-16",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 □ 8 ⊕ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_de... |
logic-v2 | Define ◎, the rules are as follows:
on the real number field, x ◎ y = y * x / x * x.
and ♡, the rules are as follows:
when y is even, x ♡ y = y * y * 1 ◎ x;
otherwise, x ♡ y = (1 - 5 ◎ y) - x.
The precedence of operations: ♡ > ◎ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression i... | {
"game_data": {
"answer": "12",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ♡ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth":... |
logic-v2 | Define ⊙, the rules are as follows:
on the real number field, x ⊙ y = 4 * x - y.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = abs(y - x - y) - 1.
and ☆, the rules are as follows:
on the real number field, x ☆ y = y - x ⊙ y.
The precedence of operations: ⊙ > ** > * = / = % = ☆ > + = - = ⊗。
Pa... | {
"game_data": {
"answer": "7",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ☆ 4 ⊗ 3 ** 7 ⊙ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nes... |
logic-v2 | Define ☆, the rules are as follows:
when x is even, x ☆ y = y - x + x;
otherwise, x ☆ y = y * x ** x.
The precedence of operations: ** > * = / = % = ☆ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 6 ☆ 4
Pl... | {
"game_data": {
"answer": "4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ☆ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": ... |
logic-v2 | 定义 △，规则如下：
实数域上，x △ y = abs(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: 6 △ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-3",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 △ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth":... |
logic-v2 | 定义 ♡，规则如下：
实数域上，x ♡ y = x - abs(x - y * y) - x。
和 ⊗，规则如下：
实数域上，x ⊗ y = abs(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: 3 ♡ 3 ⊗ 6 % 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "3",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ♡ 3 ⊗ 6 % 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_... |
logic-v2 | Define ♡, the rules are as follows:
when x is even, x ♡ y = x + y + x * y / (x);
otherwise, x ♡ y = (y - y - x - x).
and ○, the rules are as follows:
on the real number field, x ○ y = y * 1 ♡ x.
The precedence of operations: ○ > ** > * = / = % > + = - = ♡。
Parentheses have the highest priority, and the expression... | {
"game_data": {
"answer": "-6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ○ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth":... |
logic-v2 | Define ⊙, 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 - y + y).
and ▽, the rules are as follows:
on the real number field, x ▽ y = y - x ⊙ x.
The precedence of operations: ⊙ = ▽ > ** = ⊗ > * = / = % > + = -。
Parenthes... | {
"game_data": {
"answer": "5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ⊙ 6 ▽ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dep... |
logic-v2 | Define □, the rules are as follows:
on the real number field, x □ y = x - y * 5 - x + y.
and ⊙, the rules are as follows:
when y is a multiple of 3, x ⊙ y = x + x / y - x;
otherwise, x ⊙ y = y - 5 - 4 * x * 2.
The precedence of operations: ** = ⊙ > * = / = % > + = - = □。
Parentheses have the highest priority, and... | {
"game_data": {
"answer": "3888",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 □ 3 ** 4 * 1 ⊙ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"... |
logic-v2 | 定义 △，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 △ 2 △ 4 / 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1.4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 △ 2 △ 4 / 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesti... |
logic-v2 | 定义 ⊙，规则如下：
实数域上，x ⊙ y = x * x * 1 + y / y。
和 △，规则如下：
实数域上，x △ y = y ⊙ x。
和 ♢，规则如下：
当y是3的倍数时，x ♢ y = x + abs(3 + x + 1 + y)；
其他情况下，x ♢ y = abs(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 △ 1 ♢ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ⊙ 4 △ 1 ♢ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_... |
logic-v2 | Define ♡, the rules are as follows:
when y is even, x ♡ y = y + x + abs(y);
otherwise, x ♡ y = y / x.
and □, the rules are as follows:
when x is a multiple of 5, x □ y = y - x * x;
otherwise, x □ y = y * x.
The precedence of operations: □ > ** > * = / = % > + = - = ♡。
Parentheses have the highest priority, and ... | {
"game_data": {
"answer": "1.25",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 □ 2 ♡ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_d... |
logic-v2 | Define ♡, the rules are as follows:
on the real number field, x ♡ y = y * x + y.
and ⊕, the rules are as follows:
when x is odd, x ⊕ y = y * x + y;
otherwise, x ⊕ y = y * x.
The precedence of operations: ♡ > ** = ⊕ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parenthes... | {
"game_data": {
"answer": "359",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ♡ 4 ⊕ 9 - 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nestin... |
logic-v2 | Define △, the rules are as follows:
when y is even, x △ y = x + x - x * x * y;
otherwise, x △ y = 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 expr... | {
"game_data": {
"answer": "4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null... |
logic-v2 | Define ▽, the rules are as follows:
when the sum of x and y is even, x ▽ y = y - (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... | {
"game_data": {
"answer": "0.941178",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 % 3 ▽ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nest... |
logic-v2 | Define ☆, the rules are as follows:
when x is a multiple of 5, x ☆ y = y + y - x - 5 * y;
otherwise, x ☆ y = x - y * x + y * x.
and ⊙, the rules are as follows:
when y is a multiple of 3, x ⊙ y = (y ☆ y + x + y);
otherwise, x ⊙ y = (x + y).
and ♢, the rules are as follows:
on the real number field, x ♢ y = x ... | {
"game_data": {
"answer": "-18",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 + 6 ⊙ 8 ☆ 4 ♢ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"ne... |
logic-v2 | 定义 △，规则如下：
当x和y的和是偶数时，x △ y = y - y + x * y * y；
其他情况下，x △ y = abs(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 - 9 △ 6 % 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 - 9 △ 6 % 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nestin... |
logic-v2 | 定义 △，规则如下：
实数域上，x △ y = y + 5 * 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
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "24",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 △ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth":... |
logic-v2 | 定义 △，规则如下：
实数域上，x △ y = 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: 2 △ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "151",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 △ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth"... |
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: 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | 定义 ○，规则如下：
实数域上，x ○ y = y - 4 * 1 * x。
运算优先级：○ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7 ○ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-22",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ○ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth"... |
logic-v2 | Define ○, the rules are as follows:
when the sum of x and y is odd, x ○ 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 expressio... | {
"game_data": {
"answer": "49",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ○ 5 * 9 ** 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nestin... |
logic-v2 | Define ♢, the rules are as follows:
on the real number field, x ♢ y = x + x - x * y * y.
and ○, the rules are as follows:
when the sum of x and y is odd, x ○ y = y - y + y - x - x;
otherwise, x ○ y = y / x * x - y * x.
and ☆, the rules are as follows:
on the real number field, x ☆ y = y + 3 + x + x ○ 2.
The pre... | {
"game_data": {
"answer": "1500",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ☆ 6 ♢ 8 ○ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesti... |
logic-v2 | Define ◇, the rules are as follows:
when x is less than y, x ◇ y = y * x - y + x;
otherwise, x ◇ y = 3 + y / x + y.
and ♡, the rules are as follows:
on the real number field, x ♡ y = y - 4 * y + y ◇ x.
The precedence of operations: ◇ > ** > * = / = % > + = - = ♡。
Parentheses have the highest priority, and the exp... | {
"game_data": {
"answer": "4.5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ◇ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth"... |
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