env stringclasses 1
value | prompt stringlengths 119 673 | extra dict |
|---|---|---|
logic-v2 | 定义 ⊕，规则如下：
实数域上，x ⊕ y = y + x + y。
和 ◎，规则如下：
实数域上，x ◎ y = 5 * y ⊕ y * 2 - x。
和 ○，规则如下：
实数域上，x ○ y = 3 ◎ x * y。
运算优先级：◎ = ○ > ** > * = / = % = ⊕ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 ◎ 3 ⊕ 6 ○ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1652",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ◎ 3 ⊕ 6 ○ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nes... |
logic-v2 | 定义 ○，规则如下：
当x和y都是奇数时，x ○ y = y - y * x + y；
其他情况下，x ○ y = y / x - abs(x + y)。
运算优先级：** > * = / = % = ○ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 ○ 2 / 6 ** 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-0.000986",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ○ 2 / 6 ** 5",
"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 = 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 ○ 1 * 1
Please fill your... | {
"game_data": {
"answer": "88",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ○ 10 ○ 1 * 1",
"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 - x + 4 * y。
和 △，规则如下：
当y是3的倍数时，x △ y = y ⊙ x + 2 * x + x；
其他情况下，x △ y = y + 1 ⊙ (1 / x)。
和 ○，规则如下：
当x和y都是偶数时，x ○ y = y - x + x + y；
其他情况下，x ○ 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: 1 ○ 2 ⊙ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ○ 2 ⊙ 2",
"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 the sum of x and y is even, x ☆ y = y - x / 3 - x;
otherwise, x ☆ y = y - x + x * y.
and ♡, the rules are as follows:
on the real number field, x ♡ y = (y / x).
The precedence of operations: ☆ > ** = ♡ > * = / = % > + = -。
Parentheses have the highest priority, and the exp... | {
"game_data": {
"answer": "0.625",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ♡ 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:
when x is even, x □ y = y * x * y - x;
otherwise, x □ y = 4 ** y * 4 - x.
and ☆, the rules are as follows:
on the real number field, x ☆ y = x * y * y □ x.
The precedence of operations: ☆ > ** = □ > * = / = % > + = -。
Parentheses have the highest priority, and the expression in... | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ☆ 4 □ 1",
"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3的倍数时，x ♢ y = x + y - x；
其他情况下，x ♢ y = (x / x) - y * x。
和 ♡，规则如下：
当x是奇数时，x ♡ y = 1 + (y * y / x)；
其他情况下，x ♡ y = (y - x * y) ** y。
和 ⊗，规则如下：
实数域上，x ⊗ y = x - x + 2 + y。
运算优先级：** = ⊗ > * = / = % > + = - = ♢ = ♡。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 ♡ 4 ♢ 3 ⊗ 3 ♢ 6 / 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "93",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ♡ 4 ♢ 3 ⊗ 3 ♢ 6 / 2",
"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 = 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 * 7 △ 10
Please fill your... | {
"game_data": {
"answer": "-146",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 * 7 △ 10",
"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 = y - y / x。
和 ⊕，规则如下：
当y是奇数时，x ⊕ y = y ◇ x；
其他情况下，x ⊕ y = y * x * x。
和 △，规则如下：
当x大于y时，x △ 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: 7 △ 9 ◇ 8 ⊕ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "2123.851852",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 △ 9 ◇ 8 ⊕ 6",
"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 = abs(x + 1) + y.
and ⊕, the rules are as follows:
when y is a multiple of 5, x ⊕ y = y * x;
otherwise, x ⊕ y = x + y + y.
The precedence of operations: □ > ** > * = / = % = ⊕ > + = -。
Parentheses have the highest priority, and the expression ins... | {
"game_data": {
"answer": "154",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 □ 6 * 6 □ 3 ⊕ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"ne... |
logic-v2 | 定义 ♡，规则如下：
当y是奇数时，x ♡ y = x - y * x；
其他情况下，x ♡ y = x - abs(x * y) + x。
和 ◎，规则如下：
实数域上，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 ◎ 3 * 1 * 5 ♡ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-50",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ◎ 3 * 1 * 5 ♡ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"ne... |
logic-v2 | 定义 ⊙，规则如下：
实数域上，x ⊙ y = y * x + x。
和 ⊗，规则如下：
实数域上，x ⊗ y = 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 ⊙ 10 ⊗ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "124",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ⊙ 10 ⊗ 3",
"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 = y - y + y * y - x.
The precedence of operations: ** > * = / = % > + = - = ○。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 3
Please fill your fina... | {
"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 the sum of x and y is odd, x ◎ y = y / (y * x) - x;
otherwise, x ◎ y = y * 2 + x / 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 ... | {
"game_data": {
"answer": "401",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ◎ 5 ○ 8",
"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 y is even, x ◎ y = y * (x - x) - x * y;
otherwise, x ◎ y = y * x / x + y * y.
and ○, the rules are as follows:
when x and y are both even, x ○ y = abs(y - 5) - y - y / x;
otherwise, x ○ y = y + x / x.
and □, the rules are as follows:
when y is a multiple of 5, x □ y = ... | {
"game_data": {
"answer": "9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ◎ 7 ○ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dept... |
logic-v2 | Define ⊙, the rules are as follows:
when x is greater than y, x ⊙ y = y / x * 5 ** (y) * 4;
otherwise, x ⊙ y = 4 * y * x * x + x.
and ♢, the rules are as follows:
when the sum of x and y is odd, x ♢ y = y ⊙ x * x * x + (y);
otherwise, x ♢ y = y * 3 - x * y.
and ☆, the rules are as follows:
on the real number fi... | {
"game_data": {
"answer": "-2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ♢ 2 ☆ 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x和y都是偶数时，x ○ y = y * x；
其他情况下，x ○ y = 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: 2 ○ 9 ○ 6 * 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-40",
"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,
"nesti... |
logic-v2 | Define □, the rules are as follows:
when x is a multiple of 5, x □ y = y - y * y / x - x;
otherwise, x □ y = x - y - x.
and ⊙, the rules are as follows:
when x and y are both even, x ⊙ y = y / 4 - 3 - x + 5;
otherwise, x ⊙ y = x * 3 □ x * 5 - y.
The precedence of operations: □ > ** = ⊙ > * = / = % > + = -。
Pare... | {
"game_data": {
"answer": "0.545455",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 / 1 □ 8 ⊙ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"n... |
logic-v2 | 定义 ▽，规则如下：
实数域上，x ▽ y = x + y + abs(x - x - y)。
和 □，规则如下：
当x和y的和是奇数时，x □ y = 5 + y - (3 - 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: 8 ▽ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "10",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ▽ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth":... |
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: 5 △ 5 △ 2
Please fill your final an... | {
"game_data": {
"answer": "50",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 △ 5 △ 2",
"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 = x / y - y + y * y。
和 ▽，规则如下：
实数域上，x ▽ y = (y - y) - 4 / x ⊕ y。
和 ○，规则如下：
实数域上，x ○ y = y + x ▽ x - y。
运算优先级：▽ > ** > * = / = % = ⊕ > + = - = ○。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 ▽ 5 ⊕ 1 / 7 ○ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-11.632194",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ▽ 5 ⊕ 1 / 7 ○ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
... |
logic-v2 | 定义 ☆，规则如下：
当x是3的倍数时，x ☆ y = y * x + 3；
其他情况下，x ☆ y = y - y * x。
和 □，规则如下：
当x小于y时，x □ y = y ☆ x；
其他情况下，x □ y = (x) - y + x。
运算优先级：☆ > ** > * = / = % > + = - = □。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 ☆ 1 □ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "15",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ☆ 1 □ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dep... |
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 = y ** 5 * 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: 1 ⊗ 9 - 9 ♢ 7 ⊕ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "9.999941",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ⊗ 9 - 9 ♢ 7 ⊕ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
... |
logic-v2 | 定义 ◇，规则如下：
当y是5的倍数时，x ◇ y = x ** y；
其他情况下，x ◇ y = y + 3 + x。
运算优先级：** > * = / = % > + = - = ◇。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 ◇ 6 ** 6 ◇ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "46678",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ◇ 6 ** 6 ◇ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"ne... |
logic-v2 | 定义 ◎，规则如下：
当x和y都是偶数时，x ◎ y = y + y + x；
其他情况下，x ◎ y = (x) + y + x + x。
和 ☆，规则如下：
当y是3的倍数时，x ☆ y = y * x - 4；
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: 9 % 7 ◎ 8 ☆ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "10.142857",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 % 7 ◎ 8 ☆ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"... |
logic-v2 | 定义 ⊙，规则如下：
当y是5的倍数时，x ⊙ y = x * (x + y / 1)；
其他情况下，x ⊙ y = y - 2 + x。
和 ♡，规则如下：
当x是5的倍数时，x ♡ y = 2 + x ⊙ y * 1；
其他情况下，x ♡ y = x / y。
和 ☆，规则如下：
当x和y的和是偶数时，x ☆ y = x + y * x - y；
其他情况下，x ☆ y = y ⊙ x - x。
运算优先级：♡ = ☆ > ** > * = / = % > + = - = ⊙。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ♡ 7 ☆ 4 ⊙ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ♡ 7 ☆ 4 ⊙ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_... |
logic-v2 | Define ⊕, the rules are as follows:
on the real number field, x ⊕ y = abs(4 + x * y).
and ◇, the rules are as follows:
on the real number field, x ◇ y = x / x + y.
and ♡, the rules are as follows:
when the sum of x and y is odd, x ♡ y = y ◇ x;
otherwise, x ♡ y = x ** x ◇ y.
The precedence of operations: ◇ > ** ... | {
"game_data": {
"answer": "24",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ♡ 5 ⊕ 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y是5的倍数时，x ⊕ y = y + x - y；
其他情况下，x ⊕ y = y * x + y + x。
和 ◎，规则如下：
当x和y的和是奇数时，x ◎ y = (y / y) + x；
其他情况下，x ◎ y = (x) * x * x - y。
和 ◇，规则如下：
实数域上，x ◇ y = x + abs(y ** 3 - 5)。
运算优先级：⊕ > ** = ◎ > * = / = % = ◇ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 ⊕ 2 ◎ 9 ◇ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1381",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ⊕ 2 ◎ 9 ◇ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesti... |
logic-v2 | Define ○, the rules are as follows:
when x is even, x ○ y = x + 1 / 1 / y;
otherwise, x ○ y = (x * y + y - y).
The precedence of operations: ** = ○ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression:... | {
"game_data": {
"answer": "125",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 * 8 ○ 3 ○ 3",
"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 + y - x.
The precedence of operations: ** > * = / = % = ◇ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 9 / 10 ◇ 3
Please fill your fin... | {
"game_data": {
"answer": "3",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 / 10 ◇ 3",
"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 = 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: 6 ○ 1 + 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "3",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ○ 1 + 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dep... |
logic-v2 | 定义 □，规则如下：
实数域上，x □ y = y - x - x + x * y。
和 ♢，规则如下：
实数域上，x ♢ y = x / x * (x + y / x)。
运算优先级：** > * = / = % = □ = ♢ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5 ♢ 4 □ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-4.8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ♢ 4 □ 1",
"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 = y * x * (5 - y).
and ○, the rules are as follows:
when x is even, x ○ y = y * x - y + x;
otherwise, x ○ y = y ♢ x * x * x.
and △, the rules are as follows:
when x is odd, x △ y = x ** 3 + y - y;
otherwise, x △ y = x * y * y / y.
The precede... | {
"game_data": {
"answer": "-1152",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ** 7 ○ 4 △ 2 ♢ 9",
"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 = x - y - x。
和 ○，规则如下：
实数域上，x ○ y = y - x ◇ y。
和 ♢，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 + x。
运算优先级：** > * = / = % = ◇ > + = - = ○ = ♢。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 ♢ 3 ◇ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ♢ 3 ◇ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dept... |
logic-v2 | 定义 ⊙，规则如下：
实数域上，x ⊙ y = y * y * x / x。
和 ⊕，规则如下：
实数域上，x ⊕ y = x * 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 ♡ 3 ⊕ 4 ⊙ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "8125",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ♡ 3 ⊕ 4 ⊙ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesti... |
logic-v2 | Define ♡, the rules are as follows:
when x is less than y, x ♡ y = x + x / y - y * (y);
otherwise, x ♡ y = abs(y - y * 4 / x).
and ☆, the rules are as follows:
when y is a multiple of 3, x ☆ y = x - y + y ♡ y * y;
otherwise, x ☆ y = 5 ♡ x + y + x + 5.
The precedence of operations: ♡ > ** > * = / = % > + = - = ☆... | {
"game_data": {
"answer": "-57.25",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ♡ 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 = 2 ** x + y + y + x。
和 ⊗，规则如下：
实数域上，x ⊗ y = abs(y * x + y * y) * x。
和 ♢，规则如下：
当y是奇数时，x ♢ y = y - y - x；
其他情况下，x ♢ y = y * abs(1 + x)。
运算优先级：♢ > ** = ⊕ > * = / = % > + = - = ⊗。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 9 ⊗ 2 ⊕ 1 ♢ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "468",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ⊗ 2 ⊕ 1 ♢ 1",
"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 * 1。
和 ▽，规则如下：
当x是奇数时，x ▽ y = x * y ⊕ x；
其他情况下，x ▽ y = x * x / y。
和 ◇，规则如下：
实数域上，x ◇ y = y + x * y。
运算优先级：⊕ > ◇ > ** = ▽ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5 ▽ 1 - 2 ⊕ 8 ◇ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-47",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ▽ 1 - 2 ⊕ 8 ◇ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"ne... |
logic-v2 | Define ⊕, the rules are as follows:
when y is a multiple of 5, x ⊕ y = x / y;
otherwise, x ⊕ y = x * y.
and ⊗, the rules are as follows:
when x is even, x ⊗ y = x - x + y;
otherwise, 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:... | {
"game_data": {
"answer": "25.032654",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ⊕ 6 □ 1 ⊗ 2",
"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 = (x) - y ** y + y。
和 □，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。
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 ☆ 1 □ 2 ♢ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "8.0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ☆ 1 □ 2 ♢ 9",
"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 = y - 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 a multiple of 5, x ○ y = y + x / x;
otherwise, x ○ y = 3 + x / y.
The precedence of operations: ⊕ > ** = ○ > *... | {
"game_data": {
"answer": "-9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ⊕ 8 △ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dep... |
logic-v2 | Define △, the rules are as follows:
when y is odd, x △ y = 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: 10 △ 10... | {
"game_data": {
"answer": "30",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 △ 10",
"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 - 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: 2 % 5 * 3 ▽ 1
Please fill you... | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 % 5 * 3 ▽ 1",
"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 * y.
and □, the rules are as follows:
when x and y are both even, x □ y = y * x * x * y * x;
otherwise, x □ y = x + x + y + y.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = x + 2 □ x + y - y.
The precedence ... | {
"game_data": {
"answer": "16",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ♢ 2 ⊗ 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:
when x is odd, x ⊕ y = y - x - y;
otherwise, x ⊕ y = x * x * y.
and △, the rules are as follows:
when y is odd, x △ y = x * y ⊕ (x);
otherwise, x △ y = y * y * x.
and ♢, the rules are as follows:
when y is a multiple of 3, x ♢ y = (4 - x * y);
otherwise, x ♢ y = y / x - y... | {
"game_data": {
"answer": "3004",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ⊕ 6 ♢ 6 △ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nest... |
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.
The precedence of operations: ◇ > ♡ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated fi... | {
"game_data": {
"answer": "0.0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ** 8 ◇ 4 ♡ 8 ◇ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"n... |
logic-v2 | Define ♢, the rules are as follows:
when x and y are both odd, x ♢ y = x - y * x;
otherwise, x ♢ y = y * x - x.
and ♡, the rules are as follows:
on the real number field, x ♡ y = y + x * x.
and ◇, the rules are as follows:
when x is greater than y, x ◇ y = x + y + 4;
otherwise, x ◇ y = x + y.
The precedence o... | {
"game_data": {
"answer": "273",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ♡ 1 ♢ 1 ♡ 9 ◇ 4",
"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等于y时，x △ y = y * x / x；
其他情况下，x △ y = y / x + x。
和 ♡，规则如下：
实数域上，x ♡ y = 5 ** x * y。
和 ▽，规则如下：
当x和y都是偶数时，x ▽ y = y * 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: 9 △ 7 ▽ 5 ♡ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "28044.199495",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 △ 7 ▽ 5 ♡ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
... |
logic-v2 | 定义 △，规则如下：
当x和y的和是奇数时，x △ y = x - x * y * x * y；
其他情况下，x △ y = x * 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: 7 △ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-1757",
"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_dept... |
logic-v2 | Define ◇, the rules are as follows:
when x is a multiple of 3, x ◇ y = y - x - y - y;
otherwise, x ◇ y = y - x * y * x.
The precedence of operations: ** > * = / = % = ◇ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the ex... | {
"game_data": {
"answer": "-11",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ◇ 2",
"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 = y - x * 5。
运算优先级：▽ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 ▽ 5 + 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-34",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ▽ 5 + 1",
"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 = 3 * x * y - y * y.
and ⊕, the rules are as follows:
when y is even, x ⊕ y = y + y + x;
otherwise, x ⊕ y = x - x - y - y * y.
The precedence of operations: ☆ > ** = ⊕ > * = / = % > + = -。
Parentheses have the highest priority, and the expression... | {
"game_data": {
"answer": "-1256",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 + 1 ⊕ 4 ☆ 5",
"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 and y are both even, x ⊕ y = y * y - 1 - x * y;
otherwise, x ⊕ y = y - x + x.
and ⊙, the rules are as follows:
when y is a multiple of 3, x ⊙ y = y - y ⊕ x;
otherwise, x ⊙ y = y * y ⊕ x * x.
and ○, the rules are as follows:
on the real number field, x ○ y = 2 - x + y... | {
"game_data": {
"answer": "36",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ○ 10 ** 1 ⊕ 6 ⊙ 1",
"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是偶数时，x ☆ y = x ** x * y；
其他情况下，x ☆ y = x - y + 1 * y。
和 ◎，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 * 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
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "10.666667",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ◎ 8",
"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大于y时，x ○ y = x + y + y * x * x；
其他情况下，x ○ y = y / x + 2 * 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
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "55",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ○ 3",
"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 equal to y, x ◇ y = y - y + x - x + y;
otherwise, x ◇ y = y / x + 4 - y.
The precedence of operations: ◇ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the exp... | {
"game_data": {
"answer": "0.010582",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ◇ 4 / 6 / 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"n... |
logic-v2 | 定义 ◎，规则如下：
实数域上，x ◎ y = x - y - 1 / x。
和 △，规则如下：
实数域上，x △ y = 3 - y - 2 * x。
运算优先级：** > * = / = % = ◎ > + = - = △。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7 ◎ 6 △ 2 △ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-2.571429",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ◎ 6 △ 2 △ 7",
"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 = x + y - 4.
and ▽, the rules are as follows:
when x is odd, x ▽ y = x + x + y - y;
otherwise, x ▽ y = y - y - x ♢ 1.
and ◇, the rules are as follows:
on the real number field, x ◇ y = y * y + x * y.
The precedence of operations: ♢ = ▽ > ◇ > **... | {
"game_data": {
"answer": "1300",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ▽ 3 ♢ 9 ◇ 10 ◇ 10",
"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 = 1 + 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
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 | Define ☆, the rules are as follows:
on the real number field, x ☆ y = y * y * x - y.
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = y - 4 * y - x.
The precedence of operations: ☆ > ** > * = / = % = ⊙ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is cal... | {
"game_data": {
"answer": "-12",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ⊙ 3 ☆ 1 + 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 = 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: 4 ▽ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-65500",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ▽ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dep... |
logic-v2 | 定义 △，规则如下：
实数域上，x △ y = y + x - x。
运算优先级：** > * = / = % = △ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 / 8 △ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 / 8 △ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dep... |
logic-v2 | Define ♢, the rules are as follows:
on the real number field, x ♢ y = y + y * y - y + x.
and ☆, the rules are as follows:
when x is greater than y, x ☆ y = y * (y - x - y) ♢ y;
otherwise, x ☆ y = 5 ♢ 3 - y / y * x.
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = x - y / x * y + y.
The precede... | {
"game_data": {
"answer": "4.5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ⊙ 6 ☆ 9",
"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 - y * 2 * 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
Please fill your final an... | {
"game_data": {
"answer": "8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8",
"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 y is odd, x ○ y = x - y - x;
otherwise, x ○ y = (x + y * y).
The precedence of operations: ** > * = / = % = ○ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 1 ○ 3
Pl... | {
"game_data": {
"answer": "-3",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ○ 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 = y * y * x * 3.
and ☆, the rules are as follows:
when y is even, x ☆ y = y ⊙ x + x - y;
otherwise, x ☆ y = y - y * x.
and △, the rules are as follows:
when x is odd, x △ y = x - x / y + y;
otherwise, x △ y = x - 5 * y.
The precedence of oper... | {
"game_data": {
"answer": "50",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ⊙ 2 △ 2",
"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 + x + x。
和 ◎，规则如下：
当x是偶数时，x ◎ y = x + 4 * 2 * y；
其他情况下，x ◎ y = x - y □ x + y。
和 ☆，规则如下：
实数域上，x ☆ y = x * y - y。
运算优先级：** = □ = ☆ > * = / = % > + = - = ◎。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 ◎ 5 ☆ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "170",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ◎ 5 ☆ 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:
when the sum of x and y is even, x ▽ y = y + x ** y * x;
otherwise, x ▽ y = y - x * x - y.
The precedence of operations: ** > * = / = % = ▽ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of... | {
"game_data": {
"answer": "-18",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ▽ 10 + 6 + 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesti... |
logic-v2 | Define ⊗, the rules are as follows:
when y is odd, x ⊗ y = (x - y) - 1 * x;
otherwise, x ⊗ y = y + x * 5 ** (x).
and ♡, the rules are as follows:
on the real number field, x ♡ y = y / y ⊗ x.
and ⊕, the rules are as follows:
when x is a multiple of 5, x ⊕ y = (y - y - x) + 1;
otherwise, x ⊕ y = 4 / x - y - x.
... | {
"game_data": {
"answer": "4.714286",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ⊗ 7 ♡ 2 ⊕ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"n... |
logic-v2 | Define □, the rules are as follows:
on the real number field, x □ y = x - 1 + y * y.
and ♢, the rules are as follows:
when x is less than y, x ♢ y = x - abs(x + y - y - y);
otherwise, x ♢ y = y + (x) + y - y + x.
The precedence of operations: ♢ > ** > * = / = % = □ > + = -。
Parentheses have the highest priority, ... | {
"game_data": {
"answer": "3",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ♢ 6 □ 2 ♢ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_... |
logic-v2 | Define ◎, the rules are as follows:
when the sum of x and y is odd, x ◎ y = y + abs(x + 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... | {
"game_data": {
"answer": "1737",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ◎ 5 ** 6 / 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nest... |
logic-v2 | Define ◇, the rules are as follows:
on the real number field, x ◇ y = 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: 3 % 2 ◇ 8
Please fill your ... | {
"game_data": {
"answer": "3",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 % 2 ◇ 8",
"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 * y + x.
and ♢, the rules are as follows:
when x is even, x ♢ y = x ⊕ x + y;
otherwise, x ♢ y = x - 4 * y ⊕ 2.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = x / x - y.
The precedence of operations: ⊕ = ♢ > ⊗ > ** > ... | {
"game_data": {
"answer": "-183",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ⊗ 5 ⊗ 10 ♢ 8 ⊕ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"... |
logic-v2 | Define ⊕, the rules are as follows:
on the real number field, x ⊕ y = x + x / x + y / x.
and △, the rules are as follows:
when x is a multiple of 3, x △ y = x + y ⊕ y * y / x;
otherwise, x △ y = (3) * y / 3 / x * x.
and ♡, the rules are as follows:
on the real number field, x ♡ y = y + y / x * y.
The precedence... | {
"game_data": {
"answer": "8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 △ 1 ⊕ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dep... |
logic-v2 | Define △, the rules are as follows:
when the sum of x and y is odd, x △ y = y + y * x + x + y;
otherwise, x △ y = x / y + 1 - y / abs(4).
The precedence of operations: △ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate t... | {
"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 = y + (x)。
运算优先级：○ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7 + 9 ○ 1 + 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "19",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 + 9 ○ 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 = x ** y。
和 ☆，规则如下：
实数域上，x ☆ y = y - y * x。
运算优先级：** > * = / = % = ♡ > + = - = ☆。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 ♡ 7 % 10 ☆ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ♡ 7 % 10 ☆ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nestin... |
logic-v2 | Define ○, the rules are as follows:
when y is a multiple of 3, x ○ y = y + y + x + y * y;
otherwise, x ○ y = y / abs(x - x + 1).
The precedence of operations: ○ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value ... | {
"game_data": {
"answer": "10",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ○ 10 / 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：
实数域上，x ⊙ y = y + y - x。
和 ⊗，规则如下：
当y是奇数时，x ⊗ y = x - x * y；
其他情况下，x ⊗ y = x * y ⊙ y。
和 ▽，规则如下：
当y是3的倍数时，x ▽ y = (x + x) ⊗ y；
其他情况下，x ▽ y = x * y。
运算优先级：⊗ > ** > * = / = % = ⊙ > + = - = ▽。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5 ⊙ 8 ⊙ 10 ⊗ 4 ▽ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-150",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ⊙ 8 ⊙ 10 ⊗ 4 ▽ 2",
"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 + y - y * x.
and ▽, the rules are as follows:
when the sum of x and y is even, x ▽ y = y + x;
otherwise, x ▽ y = (y) - x * y.
and ☆, the rules are as follows:
on the real number field, x ☆ y = 5 + y ▽ x + y.
The precedence of operations: ⊕ ... | {
"game_data": {
"answer": "212",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ⊕ 7 ▽ 5 ☆ 2 ⊕ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"ne... |
logic-v2 | Define △, the rules are as follows:
when x is odd, x △ y = y - 2 - 5 ** 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... | {
"game_data": {
"answer": "10",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 △ 9 △ 10",
"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是3的倍数时，x ◇ y = (x - y / x)；
其他情况下，x ◇ y = y + y * (x)。
运算优先级：** > * = / = % > + = - = ◇。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 ◇ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "27",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ◇ 3",
"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 y is a multiple of 3, x ♡ y = 2 - 1 - x - y;
otherwise, x ♡ y = y * y - y / x.
and ⊗, the rules are as follows:
when y is odd, x ⊗ y = (y) + x ♡ 3;
otherwise, x ⊗ y = 5 - 5 + y * y + x.
The precedence of operations: ♡ > ** > * = / = % = ⊗ > + = -。
Parentheses have the hi... | {
"game_data": {
"answer": "55",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ♡ 3 ⊗ 9 ⊗ 6",
"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 * 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 ▽ 7
Please fill your final an... | {
"game_data": {
"answer": "70",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ▽ 7",
"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 y is a multiple of 5, x ♡ y = y - x - y;
otherwise, x ♡ y = x + y - y.
and ♢, the rules are as follows:
on the real number field, x ♢ y = x / x + y.
The precedence of operations: ♡ > ** > * = / = % = ♢ > + = -。
Parentheses have the highest priority, and the expression insi... | {
"game_data": {
"answer": "2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ♡ 2 ♡ 8 ♢ 1",
"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等于y时，x ♡ y = 3 - x - y；
其他情况下，x ♡ y = y + x - 2。
和 □，规则如下：
当x是奇数时，x □ y = y * x - 1；
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: 2 ♡ 4 ** 2 □ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "15",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ♡ 4 ** 2 □ 1",
"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 * x ** y * x.
The precedence of operations: ** > * = / = % > + = - = ◇。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 8
Please fill your final a... | {
"game_data": {
"answer": "8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8",
"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：
当x和y都是偶数时，x ☆ y = x + y；
其他情况下，x ☆ y = x * y + y + 5。
和 ⊙，规则如下：
实数域上，x ⊙ y = y + 2 * 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: 9 ☆ 5 ⊙ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "6180",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ☆ 5 ⊙ 10",
"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 a multiple of 3, x ♢ y = y - x * y + y * y;
otherwise, x ♢ y = 3 / x - y - y + x.
and ☆, the rules are as follows:
when x is less than y, x ☆ y = y * x * x ** y + x;
otherwise, x ☆ y = x + y - x + 4.
and ○, the rules are as follows:
on the real number field, x ○ y =... | {
"game_data": {
"answer": "63.6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ♢ 2 ☆ 6 ○ 10 * 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"... |
logic-v2 | 定义 △，规则如下：
当x和y都是奇数时，x △ y = 4 - y + y + x；
其他情况下，x △ y = y * x + x * y。
运算优先级：△ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 △ 6 + 7 △ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "208",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 △ 6 + 7 △ 8",
"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 = y * x * x - x + y.
and ♢, the rules are as follows:
on the real number field, x ♢ y = x / x / x ** 3 - y.
and □, the rules are as follows:
on the real number field, x □ y = (5 / x - x * y) + x.
The precedence of operations: ** = □ > * = / = % =... | {
"game_data": {
"answer": "62.037037",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ♢ 2 ◎ 3 □ 1 □ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
... |
logic-v2 | 定义 ⊗，规则如下：
当y是奇数时，x ⊗ y = 2 + x - y * x；
其他情况下，x ⊗ y = y - y + x。
和 ⊙，规则如下：
实数域上，x ⊙ y = 4 - x * y - 1。
和 ♢，规则如下：
当x是奇数时，x ♢ y = (x * x - y) ** x；
其他情况下，x ♢ y = x * 5 ** 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: 7 ⊗ 6 ⊙ 4 / 10 ♢ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "48750",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ⊗ 6 ⊙ 4 / 10 ♢ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
... |
logic-v2 | 定义 ♢，规则如下：
当y是偶数时，x ♢ y = 1 / x + abs(3 ** y)；
其他情况下，x ♢ y = (y + x) - y + 5。
运算优先级：** > * = / = % = ♢ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 + 6 ♢ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "19",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 + 6 ♢ 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:
on the real number field, x △ y = y + x / y - x * x.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = 2 ** (y / 2) - x.
and ⊙, the rules are as follows:
when x is a multiple of 5, x ⊙ y = (5 - x) ⊗ x + y;
otherwise, x ⊙ y = 3 △ x * x * y.
The precedence of o... | {
"game_data": {
"answer": "-218.0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ⊙ 1 ⊗ 4 △ 5 - 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 - y。
运算优先级：** > * = / = % > + = - = ○。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4",
"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 x is greater than y, x ♢ y = abs(x * y + y);
otherwise, x ♢ y = x - 3 + y.
and ⊗, 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 = y - y - x;
otherwise, x ◎ y ... | {
"game_data": {
"answer": "-0.899805",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ♢ 10 ◎ 1 ⊗ 2 / 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
... |
logic-v2 | Define ○, the rules are as follows:
on the real number field, x ○ y = (y ** x / y).
The precedence of operations: ○ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 8
Please fill your final ans... | {
"game_data": {
"answer": "8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8",
"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 = y / x - 4.
and ⊙, the rules are as follows:
when the sum of x and y is odd, x ⊙ y = (x - y) - y;
otherwise, x ⊙ y = (x - 2 + y).
and ♡, the rules are as follows:
when x is a multiple of 5, x ♡ y = (x) / y;
otherwise, x ♡ y = x * x + y.
The ... | {
"game_data": {
"answer": "17.111111",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ⊕ 2 ♡ 1 ** 2 ⊙ 7",
"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 = 3 + x * x / 1 - y。
和 ◎，规则如下：
实数域上，x ◎ y = y / x。
和 ○，规则如下：
当y是奇数时，x ○ y = x - x - y / 1 + 5；
其他情况下，x ○ y = x - y + 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: 2 ♢ 6 ◎ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ♢ 6 ◎ 2",
"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 x is odd, x ⊕ y = y + y - x;
otherwise, x ⊕ y = y / y + x.
and □, the rules are as follows:
when x is even, x □ y = y ⊕ x + x;
otherwise, x □ y = x + y.
and ⊗, the rules are as follows:
when y is a multiple of 5, x ⊗ y = y □ x;
otherwise, x ⊗ y = x + y + x.
The prece... | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 □ 8 ⊗ 7 ⊕ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.