env stringclasses 1
value | prompt stringlengths 119 673 | extra dict |
|---|---|---|
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 ** y - x。
和 ◎，规则如下：
当y是偶数时，x ◎ y = x ⊕ y - y；
其他情况下，x ◎ y = x * y + 4。
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: 9 □ 3 ⊕ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 □ 3 ⊕ 2",
"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 + 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
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 | 定义 ♢，规则如下：
当x是偶数时，x ♢ y = (y * y) - x；
其他情况下，x ♢ y = 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 / y。
运算优先级：◇ = ◎ > ** = ♢ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 ◎ 1 ** 5 ◇ 4 ♢ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0.03867",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ◎ 1 ** 5 ◇ 4 ♢ 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 - (5 + y + x).
The precedence of operations: ▽ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 8 ▽ 9 ▽ 7 * 9
Please fill... | {
"game_data": {
"answer": "-108",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ▽ 9 ▽ 7 * 9",
"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大于y时，x ♡ y = 5 * 5 + x + y + 5；
其他情况下，x ♡ y = 4 * x + y ** x * 4。
和 ⊙，规则如下：
当x和y都是奇数时，x ⊙ y = y ♡ x ** x + y；
其他情况下，x ⊙ y = y + (x - y) - y + x。
运算优先级：♡ > ** > * = / = % = ⊙ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 9 ♡ 7 ⊙ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "88",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ♡ 7 ⊙ 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 - abs(x) * 2 - x.
and ☆, the rules are as follows:
when x is less than y, x ☆ y = x - y - y - x;
otherwise, x ☆ y = (x ♢ y).
and ⊕, the rules are as follows:
on the real number field, x ⊕ y = x ☆ 5 - y.
The precedence of operations: ** = ☆ ... | {
"game_data": {
"answer": "-35",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ⊕ 6 ♢ 7 ☆ 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 = 5 / x - 1 - y。
和 ◇，规则如下：
当x等于y时，x ◇ y = x - x - y + 2 / x；
其他情况下，x ◇ y = x ♢ y - 5 - 1 ** x。
和 ⊕，规则如下：
实数域上，x ⊕ y = abs(y - y - x * y)。
运算优先级：♢ > ◇ > ** > * = / = % > + = - = ⊕。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5 ◇ 1 ♢ 8 ◇ 6 ⊕ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "77.5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ◇ 1 ♢ 8 ◇ 6 ⊕ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"n... |
logic-v2 | 定义 ⊗，规则如下：
实数域上，x ⊗ y = x / x + y。
和 △，规则如下：
当x和y的和是奇数时，x △ y = x * x + y；
其他情况下，x △ y = (y * y ** x)。
和 ♡，规则如下：
当x是3的倍数时，x ♡ y = abs(y) * x * y；
其他情况下，x ♡ y = y - y + x。
运算优先级：♡ > ** = ⊗ = △ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 △ 3 ♡ 9 ⊗ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "7",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 △ 3 ♡ 9 ⊗ 6",
"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 = 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: 4
Please fill your final answer... | {
"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:
on the real number field, x ⊕ y = x - y + y - abs(y) - x.
and ◎, the rules are as follows:
when y is even, x ◎ y = y / 5 / 4 ⊕ x * y;
otherwise, x ◎ y = y - y ⊕ y / x.
and ○, the rules are as follows:
on the real number field, x ○ y = y - x ⊕ 1 - y - y.
The precedence of oper... | {
"game_data": {
"answer": "-6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ○ 5 ◎ 5 ** 1 ⊕ 6",
"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 = 2 + x + (y + x)。
和 ☆，规则如下：
实数域上，x ☆ y = y ** x * 3 ⊕ x + y。
和 ◎，规则如下：
当x是5的倍数时，x ◎ y = y * y / x / 5；
其他情况下，x ◎ y = abs(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 ◎ 5 + 3 ☆ 9 + 3 ⊕ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "39397",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ◎ 5 + 3 ☆ 9 + 3 ⊕ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
... |
logic-v2 | Define ⊗, the rules are as follows:
when x and y are both even, x ⊗ y = 3 - (x / 4) + y;
otherwise, x ⊗ y = y + (y - x + y) ** y.
and ▽, the rules are as follows:
when y is a multiple of 3, x ▽ y = abs(x + y) - 3 + x;
otherwise, x ▽ y = x / x / x - y - y.
and ⊙, the rules are as follows:
when x is odd, x ⊙ y = ... | {
"game_data": {
"answer": "-169.8125",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ▽ 10 ⊙ 10 ⊗ 1",
"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 + y + 1 + y.
The precedence of operations: ▽ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 1 % 6 ▽ 2
Please fill your ... | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 % 6 ▽ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dept... |
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 - (x ⊙ x)。
和 ◎，规则如下：
当x是3的倍数时，x ◎ y = abs(x * y)；
其他情况下，x ◎ y = x * y - x。
运算优先级：** = ⊙ = ◎ > * = / = % = ♢ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 ♢ 4 ◎ 3 - 6 ⊙ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "6.25",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ♢ 4 ◎ 3 - 6 ⊙ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"n... |
logic-v2 | 定义 □，规则如下：
当x和y都是偶数时，x □ y = x - x + y；
其他情况下，x □ y = 5 * x - 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 = 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 △ 3 □ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "6.75",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 △ 3 □ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_d... |
logic-v2 | 定义 ⊕，规则如下：
当y是3的倍数时，x ⊕ y = abs(x * y + y)；
其他情况下，x ⊕ y = x * 2 * (y)。
和 ☆，规则如下：
当x等于y时，x ☆ y = abs(x) + y；
其他情况下，x ☆ y = 2 * x - y。
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 ⊕ 3 ☆ 10 ☆ 2 ⊙ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-180",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ⊕ 3 ☆ 10 ☆ 2 ⊙ 9",
"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5的倍数时，x ⊕ y = y - x / y；
其他情况下，x ⊕ y = x + x + y。
和 ♡，规则如下：
实数域上，x ♡ y = (y / x) - x。
和 ▽，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 = (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 ⊕ 7 ▽ 4 ♡ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "3.636364",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ⊕ 7 ▽ 4 ♡ 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 = 4 - y + x + x;
otherwise, x △ y = x - 5 + 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 ex... | {
"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是5的倍数时，x ○ y = y / abs(x) - y * x - y；
其他情况下，x ○ y = y * x - 3 + 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 / 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "15",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ○ 7 / 4",
"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 / 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 = y / (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: 1 ♢ 10 △ 1 ♡ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ♢ 10 △ 1 ♡ 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 = 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 - x.
The precedence of operations: ⊗ > ** > * = / = % > + = - = ♢ = □。
Parentheses ... | {
"game_data": {
"answer": "-24",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ♢ 7 □ 2",
"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和y的和是偶数时，x ⊕ y = x + y；
其他情况下，x ⊕ y = y * y + x。
和 △，规则如下：
实数域上，x △ y = y + x + x。
和 ⊗，规则如下：
实数域上，x ⊗ y = (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 ⊗ 10 ⊕ 5 △ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "235",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ⊗ 10 ⊕ 5 △ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nest... |
logic-v2 | Define ⊙, the rules are as follows:
on the real number field, x ⊙ y = x + y * y.
and ⊕, the rules are as follows:
when x is greater than y, x ⊕ y = x - y * y;
otherwise, x ⊕ y = x - y - x.
and ♡, the rules are as follows:
on the real number field, x ♡ y = y * x - x.
The precedence of operations: ♡ > ⊙ > ** > * ... | {
"game_data": {
"answer": "81",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ♡ 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 = x - y + 2 - x。
和 ▽，规则如下：
实数域上，x ▽ y = x + x ♡ y * x + y。
运算优先级：▽ > ** > * = / = % = ♡ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 ♡ 10 ▽ 4 ♡ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-7",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ♡ 10 ▽ 4 ♡ 9",
"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 + x + y.
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = y - x * y.
The precedence of operations: ⊙ > ** > * = / = % > + = - = ♡。
Parentheses have the highest priority, and the expression inside the parentheses is calculated ... | {
"game_data": {
"answer": "-25",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ⊙ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth"... |
logic-v2 | 定义 ⊙，规则如下：
当x和y的和是奇数时，x ⊙ y = y * x - y；
其他情况下，x ⊙ y = y - x - x。
和 ◇，规则如下：
实数域上，x ◇ y = y + y - x。
和 □，规则如下：
实数域上，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: 7 □ 9 ◇ 10 ⊙ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-35",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 □ 9 ◇ 10 ⊙ 3",
"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 = 1 + y * x;
otherwise, x ⊙ y = x - x + y + x + x.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = 1 - x - y / y.
and ◇, the rules are as follows:
on the real number field, x ◇ y = 4 - x ⊙ y + x / x.
The precedence of ... | {
"game_data": {
"answer": "-8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ⊗ 4 ◇ 6 ⊙ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting... |
logic-v2 | 定义 ◇，规则如下：
当y是5的倍数时，x ◇ y = x - x - y - y；
其他情况下，x ◇ y = x / y。
和 ☆，规则如下：
实数域上，x ☆ y = 3 + y * (x)。
和 ◎，规则如下：
当y是5的倍数时，x ◎ y = 3 ☆ x / y - y；
其他情况下，x ◎ y = x + 1 ☆ 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 - 3 ◇ 8 - 6 ◎ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-6.916667",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ☆ 3 - 3 ◇ 8 - 6 ◎ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,... |
logic-v2 | Define ⊗, the rules are as follows:
when x and y are both even, x ⊗ y = x + y - (y);
otherwise, x ⊗ y = (y * x) + y.
and ▽, the rules are as follows:
on the real number field, x ▽ y = y ⊗ x.
and □, the rules are as follows:
on the real number field, x □ y = x + (y - y).
The precedence of operations: ** = ⊗ = ▽ ... | {
"game_data": {
"answer": "375",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ▽ 4 □ 4 ▽ 7 * 4 ⊗ 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和y的和是偶数时，x ◎ y = x * x / y；
其他情况下，x ◎ y = y / abs(x)。
和 ⊕，规则如下：
实数域上，x ⊕ y = y ** y - x。
运算优先级：⊕ > ** > * = / = % = ◎ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 ◎ 2 ⊕ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "8.6e-05",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ◎ 2 ⊕ 6",
"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是奇数时，x □ y = x - x + y；
其他情况下，x □ y = y * 4 + x * 1。
和 ◎，规则如下：
当x和y都是奇数时，x ◎ y = (x / 4 - y)；
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: 5 □ 5 ◎ 8 + 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "176",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 □ 5 ◎ 8 + 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 = y - y + x - 4.
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = y - x + x * y.
and △, the rules are as follows:
on the real number field, x △ y = y + y * x.
The precedence of operations: ⊙ = △ > ** > * = / = % = ♢ > + = -。
Par... | {
"game_data": {
"answer": "2.4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 △ 7 ♢ 2 ⊙ 1 / 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"n... |
logic-v2 | Define ◇, the rules are as follows:
when y is even, x ◇ y = x * y + x ** y;
otherwise, x ◇ y = (x - y / x - x).
The precedence of operations: ◇ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression... | {
"game_data": {
"answer": "13164",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ◇ 8 * 2 - 6",
"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 = abs(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 calcul... | {
"game_data": {
"answer": "22",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ◎ 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 / x + 4 * x * 2.
and ○, the rules are as follows:
when x is a multiple of 5, x ○ y = y * y ** x + y;
otherwise, x ○ y = abs(x - y) + x * y.
and ▽, the rules are as follows:
on the real number field, x ▽ y = y + x - x / y + y.
The precedence... | {
"game_data": {
"answer": "306.2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ⊙ 8 ▽ 8 ○ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nest... |
logic-v2 | 定义 △，规则如下：
实数域上，x △ y = x * x + 3 + x - y。
运算优先级：△ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 9 % 9 △ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 % 9 △ 3",
"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 even, x △ y = x - y - y;
otherwise, x △ y = x / y * x.
The precedence of operations: ** > * = / = % > + = - = △。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 8 △ 3
Ple... | {
"game_data": {
"answer": "21.333333",
"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_... |
logic-v2 | 定义 ♡，规则如下：
当x是奇数时，x ♡ y = y - 3 + x + 4；
其他情况下，x ♡ y = (x + y - y) * y。
运算优先级：** > * = / = % > + = - = ♡。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 % 1 ♡ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 % 1 ♡ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dept... |
logic-v2 | 定义 △，规则如下：
当x大于y时，x △ y = x + y + x * x；
其他情况下，x △ y = y + y - x。
和 ♢，规则如下：
实数域上，x ♢ y = abs(x * y) - x + 1。
运算优先级：△ > ** = ♢ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 + 10 △ 7 ♢ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "590",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 + 10 △ 7 ♢ 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 = (y + y - y ** x).
The precedence of operations: ○ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 4 ○ 8
Please fill your f... | {
"game_data": {
"answer": "-4080",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ○ 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 * 1 + x - y.
and ⊗, the rules are as follows:
when x is a multiple of 3, x ⊗ y = y + y + y + x;
otherwise, x ⊗ y = (y / x) - y - y.
The precedence of operations: ☆ > ** > * = / = % > + = - = ⊗。
Parentheses have the highest priority, and the e... | {
"game_data": {
"answer": "-26.666667",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ☆ 10 ⊗ 1 ⊗ 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 + 3 + y * x.
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = x - y * y / x.
and ○, the rules are as follows:
when x is equal to y, x ○ y = x ⊙ y - x;
otherwise, x ○ y = y / x + x + y.
The precedence of operations: ** > * ... | {
"game_data": {
"answer": "19.847761",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ⊙ 2 % 4 ⊗ 2 ○ 6",
"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 * 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 ▽ 5 ▽ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "381",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ▽ 5 ▽ 10",
"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 = x + x - x * x / y.
and ▽, 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 = x + y + x + x ♢ x.
The precedence of operations: ◇ > ** > * = / = % = ▽ ... | {
"game_data": {
"answer": "-5897.701299",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ◇ 10 ▽ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
... |
logic-v2 | Define ♡, the rules are as follows:
when y is a multiple of 5, x ♡ y = y * y + x - y - y;
otherwise, x ♡ y = 5 + x * 3 * y - y.
and ♢, the rules are as follows:
when y is even, x ♢ y = x - y - x ♡ y - x;
otherwise, x ♢ y = y ** x ♡ y + x + x.
The precedence of operations: ♡ > ** = ♢ > * = / = % > + = -。
Parenth... | {
"game_data": {
"answer": "13",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ♡ 4",
"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 - x + y ** x).
The precedence of operations: ** > * = / = % > + = - = ▽。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 4 ▽ 7 / 3
Please fill yo... | {
"game_data": {
"answer": "27.975309",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ▽ 7 / 3",
"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 - x / y.
and ☆, the rules are as follows:
on the real number field, x ☆ y = x * y * y.
and ▽, the rules are as follows:
when x is even, x ▽ y = y + x ⊕ x;
otherwise, x ▽ y = y - y / x.
The precedence of operations: ⊕ > ** = ▽ > * = / = % = ... | {
"game_data": {
"answer": "50",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ⊕ 4 % 1 ☆ 2 ▽ 9",
"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 equal to y, x ◇ y = x + 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: 4
P... | {
"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 x and y are both odd, x ○ y = x + x + x - y + y;
otherwise, x ○ y = y ** x * y.
The precedence of operations: ○ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the e... | {
"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：
实数域上，x ⊙ y = y + x。
和 ○，规则如下：
实数域上，x ○ y = x - y - y + 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: 5 ♡ 2 ○ 1 ⊙ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "142",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ♡ 2 ○ 1 ⊙ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nestin... |
logic-v2 | Define ⊕, the rules are as follows:
when x is a multiple of 3, x ⊕ y = y + y * y + x - 5;
otherwise, x ⊕ y = x - y * y / y + x.
and ♢, the rules are as follows:
on the real number field, x ♢ y = (x) * y + x - y.
and □, the rules are as follows:
on the real number field, x □ y = y * y - 2 + x.
The precedence of ... | {
"game_data": {
"answer": "2166",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ** 3 ♢ 9 ⊕ 2 □ 2",
"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都是偶数时，x ▽ y = x * y；
其他情况下，x ▽ y = x - y * 4。
运算优先级：** > * = / = % > + = - = ▽。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ▽ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-3",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ▽ 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:
when x is less than y, x ☆ y = y + x;
otherwise, x ☆ y = y - x - x.
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 p... | {
"game_data": {
"answer": "-9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ☆ 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:
when x is a multiple of 3, x ○ y = 2 + x + x * x * y;
otherwise, x ○ y = y / abs(x * x / x).
The precedence of operations: ** > * = / = % = ○ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value ... | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1",
"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 + x.
and ♡, the rules are as follows:
when x is less than y, x ♡ y = (y - 5 ☆ x) + x;
otherwise, x ♡ y = 2 / y * 1 - x.
The precedence of operations: ** > * = / = % > + = - = ☆ = ♡。
Parentheses have the highest priority, and the expressi... | {
"game_data": {
"answer": "-64",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ☆ 8 ** 2 ♡ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesti... |
logic-v2 | Define ⊕, the rules are as follows:
on the real number field, x ⊕ y = x * x / x - x / y.
and ▽, the rules are as follows:
on the real number field, x ▽ y = y / x ⊕ y + x.
and ○, the rules are as follows:
on the real number field, x ○ y = abs(x + x) * x * y.
The precedence of operations: ○ > ** = ▽ > * = / = % = ⊕... | {
"game_data": {
"answer": "8.100446",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ▽ 9 ⊕ 4 ○ 6",
"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等于y时，x ♢ y = x - x - x - y；
其他情况下，x ♢ y = x + y * y - y + y。
和 ○，规则如下：
当x和y的和是奇数时，x ○ y = y - x - y ♢ y + y；
其他情况下，x ○ y = 1 * 2 + 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 ♢ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-20",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ○ 3 ♢ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_d... |
logic-v2 | 定义 □，规则如下：
当x大于y时，x □ y = y * x - 4 + 4 / x；
其他情况下，x □ y = y * y + x + x。
和 ⊙，规则如下：
实数域上，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: 2 ⊙ 1 / 6 □ 8 □ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "234",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ⊙ 1 / 6 □ 8 □ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"n... |
logic-v2 | Define ♡, the rules are as follows:
on the real number field, x ♡ y = y * x / y + x.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = y - 2 - y * x.
and ◎, the rules are as follows:
when y is a multiple of 3, x ◎ y = x ♡ x + y + x;
otherwise, x ◎ y = x - x + y * y.
The precedence of operations... | {
"game_data": {
"answer": "-340",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ◎ 5 ⊗ 7 ♡ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesti... |
logic-v2 | Define ▽, the rules are as follows:
on the real number field, x ▽ y = y - x * x / y.
The precedence of operations: ** = ▽ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 10 ▽ 9
Please fill your fin... | {
"game_data": {
"answer": "-2.111111",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ▽ 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y是偶数时，x ◇ y = 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: 3 ◇ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "30",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ◇ 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：
当y是5的倍数时，x ⊙ y = y / x + y + x - y；
其他情况下，x ⊙ y = x + y + x。
和 ♡，规则如下：
当y是5的倍数时，x ♡ y = x * y ⊙ x；
其他情况下，x ♡ y = x + y - y ⊙ y + x。
和 □，规则如下：
实数域上，x □ y = y - y + y + y + x。
运算优先级：⊙ > ** = ♡ > * = / = % = □ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 ♡ 5 □ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "76",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ♡ 5 □ 3",
"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 = 1 / y * 1 ** x.
The precedence of operations: ○ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 4
Please fill your final a... | {
"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:
on the real number field, x ○ y = y * x + y.
The precedence of operations: ** > * = / = % = ○ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 9 ○ 9 - 1 - 2
Please fill your ... | {
"game_data": {
"answer": "87",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ○ 9 - 1 - 2",
"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 = 2 + abs(3 + y) * y * x。
和 ▽，规则如下：
实数域上，x ▽ y = (y - x + x + y * y)。
运算优先级：▽ > ** > * = / = % = □ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 / 3 □ 3 + 9 ▽ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "20",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 / 3 □ 3 + 9 ▽ 3",
"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小于y时，x ○ y = abs(y / x * y)；
其他情况下，x ○ y = x + x + (y)。
运算优先级：** > * = / = % = ○ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5 ○ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "13",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ○ 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 = x ** (x + x * x + y);
otherwise, x ⊗ y = x / 5 - y - x + x.
and ◇, the rules are as follows:
on the real number field, x ◇ y = 2 + 4 + y / x - 1.
and △, the rules are as follows:
on the real number field, x △ y = y ◇ y - 5 + x / x.
The precedence... | {
"game_data": {
"answer": "-1.8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ⊗ 7 △ 3 ◇ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesti... |
logic-v2 | Define ○, the rules are as follows:
on the real number field, x ○ y = (x / 3) * y.
The precedence of operations: ○ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 4 * 1 ○ 3 - 10
Please fill yo... | {
"game_data": {
"answer": "-6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 * 1 ○ 3 - 10",
"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 + y + x。
和 ▽，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 ▽ y - x / x；
其他情况下，x □ y = 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: 8 □ 2 / 8 ▽ 6 - 5 ⊙ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-35.589286",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 □ 2 / 8 ▽ 6 - 5 ⊙ 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 = x - y * x.
The precedence of operations: ◇ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 7 * 9 ◇ 1
Please fill your fina... | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 * 9 ◇ 1",
"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 = 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: 7
Please fill your final answer... | {
"game_data": {
"answer": "7",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7",
"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 + 3。
和 ⊕，规则如下：
当y是奇数时，x ⊕ y = x * y - (y)；
其他情况下，x ⊕ y = x ◎ x - y。
运算优先级：◎ > ** = ⊕ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 ⊕ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "3",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ⊕ 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 greater than y, x ⊙ y = y + x - y - x + x;
otherwise, x ⊙ y = x + 1 - 2 + y * x.
and ♢, the rules are as follows:
on the real number field, x ♢ y = y + 3 + 2 - y - x.
and ⊕, the rules are as follows:
on the real number field, x ⊕ y = 2 ** y + y ♢ x.
The precedence o... | {
"game_data": {
"answer": "32",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ♢ 10 ⊙ 7 % 4 ⊕ 5",
"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 even, x ◎ y = x / 4 - y;
otherwise, x ◎ y = x / y.
and ♡, the rules are as follows:
when x is less than y, x ♡ y = (x * y / y);
otherwise, x ♡ y = y + (x + y).
The precedence of operations: ** = ◎ = ♡ > * = / = % > + = -。
Parentheses have the highest priority, and t... | {
"game_data": {
"answer": "26",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ♡ 8",
"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 = x + 1 * x + y。
运算优先级：** > * = / = % = ○ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 ○ 5 / 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "3.25",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ○ 5 / 4",
"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 - x - x * y.
and ◎, the rules are as follows:
when x is a multiple of 5, x ◎ y = x + y;
otherwise, x ◎ y = x - (y) - x + y - x.
and ○, the rules are as follows:
when x is equal to y, x ○ y = x ◎ 2 - 3 - y - y;
otherwise, x ○ y = y +... | {
"game_data": {
"answer": "-2790",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ◎ 7 ○ 5 ⊕ 7 * 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
... |
logic-v2 | Define △, the rules are as follows:
when y is even, x △ y = y + abs(x / 4);
otherwise, x △ y = x ** y - x + y.
The precedence of operations: ** = △ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression:... | {
"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 | Define ♢, the rules are as follows:
when the sum of x and y is even, x ♢ y = (x * y + x);
otherwise, x ♢ y = x + abs(x - y).
and ◇, the rules are as follows:
when x is greater than y, x ◇ y = x ♢ y + y;
otherwise, x ◇ y = y + (x / y).
and ◎, the rules are as follows:
on the real number field, x ◎ y = x + y ◇ ... | {
"game_data": {
"answer": "57",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ◇ 2 ♢ 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:
when x and y are both odd, x ▽ y = x * y - y;
otherwise, x ▽ y = 3 * y - x.
The precedence of operations: ▽ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression... | {
"game_data": {
"answer": "25",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ▽ 8 + 3",
"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 less than y, x ◇ y = x - y - y * y ** y;
otherwise, x ◇ y = x - x * x + y * x.
The precedence of operations: ◇ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of t... | {
"game_data": {
"answer": "-33",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ◇ 1 + 2",
"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 = x ** x * y / x;
otherwise, x ⊗ y = x - x + y * y.
and ▽, the rules are as follows:
when x and y are both odd, x ▽ y = x + y + y ⊗ x;
otherwise, x ▽ y = y - x + x.
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = y ⊗ x.
The... | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ⊙ 3 ⊗ 6 ▽ 7",
"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 is equal to y, x □ y = x - x ** x * y * x;
otherwise, x □ y = (y / y / y - x / y).
and ☆, the rules are as follows:
on the real number field, x ☆ y = x - y - y / x - x.
The precedence of operations: ☆ > ** > * = / = % > + = - = □。
Parentheses have the highest priority, a... | {
"game_data": {
"answer": "-1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 □ 7",
"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 * 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
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 | 定义 ○，规则如下：
当y是5的倍数时，x ○ y = x * x - 1 + y；
其他情况下，x ○ y = x + x + y - (x)。
运算优先级：○ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 * 1 - 8 ○ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 * 1 - 8 ○ 1",
"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(y - x) - x.
The precedence of operations: ** = ▽ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 7 ▽ 9
Please fill your fin... | {
"game_data": {
"answer": "-5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ▽ 9",
"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 odd, x ○ y = 1 - y - y - x / x;
otherwise, x ○ y = y + x * x * 2 ** x.
The precedence of operations: ** > * = / = % > + = - = ○。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expre... | {
"game_data": {
"answer": "2308.2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ○ 6 - 9 / 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nes... |
logic-v2 | 定义 ♢，规则如下：
当x是3的倍数时，x ♢ y = y * x；
其他情况下，x ♢ y = x * y。
和 ⊙，规则如下：
实数域上，x ⊙ y = y + x。
和 ○，规则如下：
实数域上，x ○ y = abs(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 ○ 8 ♢ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "72",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ○ 8 ♢ 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：
当x是3的倍数时，x ◎ y = x + y；
其他情况下，x ◎ y = y / 2 + 3 - 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: 3 ◎ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "12",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ◎ 9",
"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 and y are both even, x ⊙ y = x + x + y;
otherwise, x ⊙ y = y * x - y.
and △, the rules are as follows:
on the real number field, x △ y = x ** y - 2.
and ▽, the rules are as follows:
when x is greater than y, x ▽ y = y + x + y;
otherwise, x ▽ y = y * x * x.
The preced... | {
"game_data": {
"answer": "340",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ▽ 1 ⊙ 6 △ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nestin... |
logic-v2 | 定义 ◇，规则如下：
当x是5的倍数时，x ◇ y = x + y / x；
其他情况下，x ◇ y = y - 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: 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8",
"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.
The precedence of operations: ** = ○ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 8 ○ 1
Please fill your f... | {
"game_data": {
"answer": "-8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ○ 1",
"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 = 2 - 1 / x * 5 + y。
运算优先级：** > * = / = % > + = - = ◇。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6",
"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 a multiple of 5, x □ y = y * 4 * x - x;
otherwise, x □ y = x / y + y + y.
and ◇, the rules are as follows:
on the real number field, x ◇ y = x * y - x.
The precedence of operations: ** > * = / = % = □ = ◇ > + = -。
Parentheses have the highest priority, and the express... | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 □ 6 ◇ 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大于y时，x △ y = x + y；
其他情况下，x △ y = y * 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: 9 △ 10 △ 8 * 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1512",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 △ 10 △ 8 * 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nest... |
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 x and y are both odd, x ☆ y = y + 5 ◎ x;
otherwise, x ☆ y = x ◎ (y - x) * x + x.
The precedence of operations: ☆ > ** > * = / = % > + = - = ◎。
Parentheses have the highest priority, and t... | {
"game_data": {
"answer": "-15",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ☆ 6 / 10 ◎ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesti... |
logic-v2 | 定义 ☆，规则如下：
实数域上，x ☆ y = abs(y) ** x。
和 ▽，规则如下：
当x小于y时，x ▽ y = x * y - x ☆ x；
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: 3 / 4 ☆ 2 ▽ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "8.0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 / 4 ☆ 2 ▽ 4",
"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 * (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:
on the real number field, x ☆ y = x + y.
and ◎, the rules are as follows:
when y is odd, x ◎ y = x ☆ y - (1);
otherwise, x ◎ y = x * (y).
The precedence of operations: ☆ = ◎ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parenthes... | {
"game_data": {
"answer": "5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 % 10 ☆ 6 ◎ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting... |
logic-v2 | 定义 ⊕，规则如下：
当y是奇数时，x ⊕ y = abs(y + x)；
其他情况下，x ⊕ y = y ** abs(x / y - 5 / y)。
和 ♢，规则如下：
实数域上，x ♢ y = (x) ⊕ y + 5 - y - x。
和 ⊗，规则如下：
当x等于y时，x ⊗ y = y ♢ 1 - x；
其他情况下，x ⊗ y = y ♢ x。
运算优先级：⊕ = ⊗ > ** = ♢ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 ♢ 5 ⊗ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-5.373472",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ♢ 5 ⊗ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nest... |
logic-v2 | 定义 ○，规则如下：
当x和y的和是奇数时，x ○ y = abs(x - y) - y；
其他情况下，x ○ y = y - x + x。
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 ⊕ 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 ○ 5 ♢ 10 ⊕ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ○ 5 ♢ 10 ⊕ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting... |
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