env stringclasses 1
value | prompt stringlengths 119 673 | extra dict |
|---|---|---|
logic-v2 | 定义 ☆，规则如下：
实数域上，x ☆ y = (x) * 2 / 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 + 10 ☆ 10 * 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0.22",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 + 10 ☆ 10 * 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"ne... |
logic-v2 | Define ♢, the rules are as follows:
on the real number field, x ♢ y = x - x + x * y - abs(x).
and ☆, the rules are as follows:
when x is odd, x ☆ y = 4 * x / y * y - y;
otherwise, x ☆ y = x + y * x + y.
and ▽, the rules are as follows:
when y is odd, x ▽ y = y + y * x - 1 ☆ y;
otherwise, x ▽ y = y - y ☆ x * 5... | {
"game_data": {
"answer": "11",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ☆ 1 ▽ 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：
实数域上，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: 4 ▽ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "36",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ▽ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth":... |
logic-v2 | Define ⊙, the rules are as follows:
when the sum of x and y is even, x ⊙ y = x + y + y ** x;
otherwise, x ⊙ y = x + y - y / y.
and ◎, the rules are as follows:
when x is odd, x ◎ y = y ⊙ x - x / y - 2;
otherwise, x ◎ y = y * y * y * x - x.
and ♢, the rules are as follows:
on the real number field, x ♢ y = x *... | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ♢ 4 ⊙ 4 ◎ 1",
"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 greater than y, x ◇ y = y * y + 1 + x;
otherwise, x ◇ y = x * y.
The precedence of operations: ◇ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression:... | {
"game_data": {
"answer": "30",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 + 4 + 2 ◇ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nestin... |
logic-v2 | 定义 ◎，规则如下：
实数域上，x ◎ y = x * y ** x * x - y。
和 △，规则如下：
实数域上，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: 7 % 9 % 8 ◎ 4 △ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "22",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 % 9 % 8 ◎ 4 △ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nes... |
logic-v2 | 定义 ○，规则如下：
实数域上，x ○ y = abs(x + y) - 3。
运算优先级：** = ○ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5 % 5 % 1 ○ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 % 5 % 1 ○ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_... |
logic-v2 | 定义 ⊕，规则如下：
实数域上，x ⊕ y = y * x + y + 1。
和 ▽，规则如下：
实数域上，x ▽ y = (y + y) * y - x。
和 ☆，规则如下：
当x和y都是奇数时，x ☆ y = x ▽ y；
其他情况下，x ☆ y = 2 / y ▽ y / x。
运算优先级：** = ⊕ = ☆ > * = / = % > + = - = ▽。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 ☆ 2 ⊕ 5 ▽ 4 % 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-2.111111",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ☆ 2 ⊕ 5 ▽ 4 % 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
... |
logic-v2 | Define ▽, the rules are as follows:
when the sum of x and y is odd, x ▽ y = y + x ** y + x;
otherwise, x ▽ y = abs(3 * y + x) + x / x.
The precedence of operations: ** > * = / = % = ▽ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the ... | {
"game_data": {
"answer": "13.666667",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 / 3 ▽ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nest... |
logic-v2 | Define △, the rules are as follows:
when x is even, x △ y = 4 / y ** x;
otherwise, x △ y = abs(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
P... | {
"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 + 1。
和 ☆，规则如下：
实数域上，x ☆ y = x * 3 ○ 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 ○ 4 □ 9 ☆ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "5193",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ○ 4 □ 9 ☆ 6",
"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 equal to y, x ♡ y = abs(y + y) + x;
otherwise, x ♡ y = x - x * y.
and □, the rules are as follows:
when x and y are both even, x □ y = y + x;
otherwise, x □ y = x ♡ y.
The precedence of operations: ** > * = / = % = ♡ = □ > + = -。
Parentheses have the highest priorit... | {
"game_data": {
"answer": "-36",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 □ 2 ♡ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_d... |
logic-v2 | 定义 △，规则如下：
实数域上，x △ y = y / 1 / x + x。
运算优先级：** > * = / = % = △ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 △ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "10.6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 △ 6",
"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等于y时，x ○ y = x + y + x - x - x；
其他情况下，x ○ y = x * y / abs(y) * x + x。
运算优先级：○ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6
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 | 定义 ⊗，规则如下：
当x是奇数时，x ⊗ y = x / y；
其他情况下，x ⊗ y = y ** y + x。
和 ♢，规则如下：
当x是奇数时，x ♢ y = y / x * y；
其他情况下，x ♢ y = y - x * y。
和 ⊕，规则如下：
当y是3的倍数时，x ⊕ 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 ♢ 1 ⊕ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1.142857",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ♢ 1 ⊕ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesti... |
logic-v2 | 定义 ⊙，规则如下：
实数域上，x ⊙ y = y * x * y。
和 ☆，规则如下：
实数域上，x ☆ y = abs(y - x + y)。
和 ♡，规则如下：
当y是3的倍数时，x ♡ y = x - y * (x + x + x)；
其他情况下，x ♡ y = 4 ☆ 3 * 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 ☆ 4 ⊙ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "96",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ☆ 4 ⊙ 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：
当x是奇数时，x △ y = y * x；
其他情况下，x △ y = x - x - y + x + x。
运算优先级：△ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 △ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 △ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth":... |
logic-v2 | Define ♢, the rules are as follows:
on the real number field, x ♢ y = x * y + y + y.
and ⊕, the rules are as follows:
on the real number field, x ⊕ y = y + 1 / x + 1.
and ▽, the rules are as follows:
on the real number field, x ▽ y = x + y * y.
The precedence of operations: ⊕ > ** > * = / = % = ▽ > + = - = ♢。
Par... | {
"game_data": {
"answer": "79.2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ♢ 5 ⊕ 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 = abs(y + x) + y.
The precedence of operations: ** > * = / = % = ▽ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 3 ▽ 1
Please fill your fin... | {
"game_data": {
"answer": "5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ▽ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": ... |
logic-v2 | Define ⊕, the rules are as follows:
when x and y are both even, x ⊕ y = x / abs(y * y) * 2;
otherwise, x ⊕ y = y + x * y - x.
and ♢, the rules are as follows:
when y is odd, x ♢ y = 5 - y * x;
otherwise, x ♢ y = y - x - x.
and □, the rules are as follows:
when y is even, x □ y = 5 - x / y;
otherwise, x □ y = ... | {
"game_data": {
"answer": "38",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 □ 7 ♢ 4 ⊕ 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 = y - x ** x - x + x。
运算优先级：** > * = / = % > + = - = ○。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 ○ 1 ○ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "7",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ○ 1 ○ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dept... |
logic-v2 | Define ⊗, the rules are as follows:
when x is equal to y, x ⊗ y = (y / x - x) ** x - x;
otherwise, x ⊗ y = x + x - x + y - 2.
and □, the rules are as follows:
when x is even, x □ y = y - y / x ⊗ y / x;
otherwise, x □ y = x * y + y - x + x.
and ♡, the rules are as follows:
when x and y are both odd, x ♡ y = x ... | {
"game_data": {
"answer": "8.9375",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 □ 5 ⊗ 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 odd, x ♡ y = x / x / y;
otherwise, x ♡ y = y * 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 expression inside the paren... | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ♡ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": ... |
logic-v2 | Define ☆, the rules are as follows:
when x and y are both even, x ☆ y = y - (x * 4);
otherwise, x ☆ y = x * y * 1.
and ⊕, the rules are as follows:
when x is greater than y, x ⊕ y = x ☆ y;
otherwise, x ⊕ y = y + x.
The precedence of operations: ⊕ > ** > * = / = % > + = - = ☆。
Parentheses have the highest priori... | {
"game_data": {
"answer": "324",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ☆ 9 ☆ 1 ⊕ 8",
"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 - y * y + x。
和 ⊗，规则如下：
当x和y的和是偶数时，x ⊗ y = y * x / y ♢ y + x；
其他情况下，x ⊗ y = x + y + x ♢ y。
和 ◎，规则如下：
当y是3的倍数时，x ◎ y = 1 + y * x；
其他情况下，x ◎ y = x - y - x - x + x。
运算优先级：♢ = ⊗ > ◎ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 ⊗ 9 ♢ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-94",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ⊗ 9 ♢ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_de... |
logic-v2 | Define □, the rules are as follows:
on the real number field, x □ y = y * x + 1 + x * x.
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 expression inside the parentheses is calcula... | {
"game_data": {
"answer": "41",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 □ 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 the sum of x and y is odd, x □ y = y + 3 * x;
otherwise, x □ y = abs(x + y + x).
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 expre... | {
"game_data": {
"answer": "16",
"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_depth":... |
logic-v2 | Define ◎, the rules are as follows:
when the sum of x and y is odd, x ◎ y = y - x - x - y;
otherwise, x ◎ y = x + x + 5 + y.
and ♢, the rules are as follows:
on the real number field, x ♢ y = y * abs(2 * x).
The precedence of operations: ◎ > ** > * = / = % > + = - = ♢。
Parentheses have the highest priority, and t... | {
"game_data": {
"answer": "-520",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 + 9 ♢ 10 ◎ 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 - y.
The precedence of operations: △ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 3 / 5 △ 3 - 8
Please fill y... | {
"game_data": {
"answer": "-7.8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 / 5 △ 3 - 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesti... |
logic-v2 | Define ☆, the rules are as follows:
when x and y are both even, x ☆ y = y * x - y * y;
otherwise, x ☆ y = y ** x + x * x.
and ◇, the rules are as follows:
on the real number field, x ◇ y = (x) + x ☆ 4 + y.
The precedence of operations: ☆ > ◇ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the... | {
"game_data": {
"answer": "12",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ☆ 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 = x + 1 + y + abs(4 + y).
and ○, the rules are as follows:
on the real number field, x ○ y = x * y - 5.
The precedence of operations: ♡ > ** > * = / = % > + = - = ○。
Parentheses have the highest priority, and the expression inside the parentheses i... | {
"game_data": {
"answer": "145",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ♡ 7 ○ 6",
"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 and y are both even, x ♢ y = x - y * (x) - y;
otherwise, x ♢ y = (x) * y - 3.
and ⊙, the rules are as follows:
when the sum of x and y is odd, x ⊙ y = x - x - 3 + y;
otherwise, x ⊙ y = y * x ♢ 3.
and □, the rules are as follows:
on the real number field, x □ y = (x) ... | {
"game_data": {
"answer": "32",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 □ 8 ♢ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dep... |
logic-v2 | Define ♢, the rules are as follows:
on the real number field, x ♢ y = (y + y + x) + 5 + 4.
and △, the rules are as follows:
when x is a multiple of 3, x △ y = 4 + y - x * 2 - x;
otherwise, x △ y = x - 4 - 2 / y + 3.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = y - x * y - y - x.
The preced... | {
"game_data": {
"answer": "522",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ♢ 4 ⊗ 8 △ 5",
"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 is a multiple of 5, x ▽ y = y ** y * x ** y;
otherwise, x ▽ y = 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 o... | {
"game_data": {
"answer": "88",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ▽ 4 * 7",
"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。
和 ○，规则如下：
实数域上，x ○ y = (4 □ 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 + 4 □ 5 / 5 ○ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "10.085294",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 + 4 □ 5 / 5 ○ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
... |
logic-v2 | 定义 ▽，规则如下：
当x是偶数时，x ▽ y = y - 5 - y + x；
其他情况下，x ▽ y = y - abs(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 ▽ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-1",
"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_depth":... |
logic-v2 | 定义 □，规则如下：
实数域上，x □ y = x * y * y + x - y。
和 ⊕，规则如下：
当x是5的倍数时，x ⊕ y = y * x - (x)；
其他情况下，x ⊕ y = 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 □ 2 % 1 ⊕ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "3",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 □ 2 % 1 ⊕ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_... |
logic-v2 | 定义 □，规则如下：
实数域上，x □ y = y + x。
和 ☆，规则如下：
实数域上，x ☆ y = (x) □ y + x。
运算优先级：☆ > □ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 9 □ 7 % 9 ☆ 5 □ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "16",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 □ 7 % 9 ☆ 5 □ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nes... |
logic-v2 | Define ♢, the rules are as follows:
when the sum of x and y is odd, x ♢ y = (y * x) * x;
otherwise, x ♢ y = y - x + x.
and ⊗, the rules are as follows:
when x is less than y, x ⊗ y = y - x / y;
otherwise, x ⊗ y = x * y * x.
The precedence of operations: ** = ♢ = ⊗ > * = / = % > + = -。
Parentheses have the highe... | {
"game_data": {
"answer": "9.8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ♢ 6 ** 5 ♢ 2 ⊗ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"... |
logic-v2 | 定义 ○，规则如下：
当x是偶数时，x ○ y = y / y - x * y；
其他情况下，x ○ y = y / x / x + x + x。
运算优先级：○ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 9 ** 6 ○ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0.0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ** 6 ○ 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x是3的倍数时，x ♡ y = x - x * y；
其他情况下，x ♡ y = y * x + (x)。
和 ⊕，规则如下：
当y是偶数时，x ⊕ y = x - y - y；
其他情况下，x ⊕ y = y * x + 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: 2 ♡ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "12",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ♡ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth":... |
logic-v2 | 定义 ◎，规则如下：
当y是5的倍数时，x ◎ y = y * (x + 2)；
其他情况下，x ◎ y = y + x - x。
和 ☆，规则如下：
当y是奇数时，x ☆ y = (y * y - x) - x；
其他情况下，x ☆ y = y * y - x ◎ y。
和 ⊕，规则如下：
当y是3的倍数时，x ⊕ y = x * y + y * y；
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: 2 ☆ 6 ⊕ 4 ◎ 10
请将最终答案填入\... | {
"game_data": {
"answer": "3860",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ☆ 6 ⊕ 4 ◎ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nest... |
logic-v2 | 定义 ⊙，规则如下：
实数域上，x ⊙ y = y - x + abs(x)。
和 □，规则如下：
当x是3的倍数时，x □ y = y / x * y + x - y；
其他情况下，x □ y = (y / x) + x ⊙ y * x。
和 ♡，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 = 3 □ 3 - 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: 4 ⊙ 8 ♡ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "37",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ⊙ 8 ♡ 3",
"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 * x.
and ◎, the rules are as follows:
when the sum of x and y is even, x ◎ y = y - y + x;
otherwise, x ◎ y = y + x ** x.
The precedence of operations: □ = ◎ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expressi... | {
"game_data": {
"answer": "-0.0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 / 8 ◎ 8 ◎ 3 □ 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和y都是偶数时，x ☆ y = y * x；
其他情况下，x ☆ y = x * y * x。
和 ⊗，规则如下：
实数域上，x ⊗ y = 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: 7 ⊗ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "13",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ⊗ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth":... |
logic-v2 | 定义 ♡，规则如下：
当y是偶数时，x ♡ y = x / 5 * x + x - y；
其他情况下，x ♡ y = x * y + x * y - y。
和 ◇，规则如下：
实数域上，x ◇ y = y ♡ y / x。
运算优先级：◇ > ♡ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5 ◇ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ◇ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": ... |
logic-v2 | 定义 △，规则如下：
当x和y都是奇数时，x △ y = y - x * x + x；
其他情况下，x △ y = 3 ** 1 * y - 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: 2 △ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "22",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 △ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth":... |
logic-v2 | 定义 ♡，规则如下：
实数域上，x ♡ y = x * x + y * x。
和 ☆，规则如下：
实数域上，x ☆ y = y - y - y * x。
运算优先级：** = ☆ > * = / = % = ♡ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 ☆ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-16",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ☆ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth"... |
logic-v2 | Define □, the rules are as follows:
when x is odd, x □ y = y + 3 / x;
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: □ > ** > * = / = % = ♡ > + = -。
Parentheses have the highest priority, and the expression inside the pare... | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ♡ 4 □ 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：
当x是奇数时，x △ y = y - x - y * x；
其他情况下，x △ y = y * y + 4 + x * x。
运算优先级：** > * = / = % = △ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7 △ 7 △ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "399",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 △ 7 △ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_de... |
logic-v2 | 定义 ☆，规则如下：
当x是奇数时，x ☆ y = y - x / x；
其他情况下，x ☆ y = 3 / x - y。
和 △，规则如下：
实数域上，x △ y = x + y - x * y。
运算优先级：☆ > ** > * = / = % > + = - = △。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 * 2 ☆ 4 △ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "43",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 * 2 ☆ 4 △ 3",
"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 = x ** x + x * y;
otherwise, x ⊗ y = x - y + y / x.
and ☆, the rules are as follows:
on the real number field, x ☆ y = (4 / y) - x.
and □, the rules are as follows:
on the real number field, x □ y = y / x ⊗ x - y - 2.
The precedence of operati... | {
"game_data": {
"answer": "-2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ☆ 2 ⊗ 9 □ 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 = 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: 7 / 10 ◇ 4
Please fill your fin... | {
"game_data": {
"answer": "0.175",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 / 10 ◇ 4",
"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 + y - x * y + 4；
其他情况下，x ⊗ y = 3 △ x * y * 3。
和 ⊕，规则如下：
实数域上，x ⊕ y = x ⊗ y * x + x - y。
运算优先级：⊗ > ** = △ = ⊕ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ⊕ 6 ⊗ 4 △ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "2525",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ⊕ 6 ⊗ 4 △ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesti... |
logic-v2 | 定义 ▽，规则如下：
实数域上，x ▽ y = (x + y + x) - y。
运算优先级：** > * = / = % > + = - = ▽。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 ▽ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ▽ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": ... |
logic-v2 | 定义 ◎，规则如下：
实数域上，x ◎ y = x - 1 + (y)。
和 ☆，规则如下：
当x和y的和是偶数时，x ☆ y = y * x ◎ x + x；
其他情况下，x ☆ y = x + (y)。
运算优先级：** > * = / = % = ◎ = ☆ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 - 1 - 5 ☆ 6 ◎ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-12",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 - 1 - 5 ☆ 6 ◎ 5",
"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等于y时，x ⊕ y = x + y * 3 - y；
其他情况下，x ⊕ y = y * y - x - x。
和 ♡，规则如下：
实数域上，x ♡ y = x ⊕ y + y - y * 5。
和 ◇，规则如下：
实数域上，x ◇ y = y * 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: 3 ◇ 7 ⊕ 2 ♡ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "9375",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ◇ 7 ⊕ 2 ♡ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesti... |
logic-v2 | 定义 △，规则如下：
当x是偶数时，x △ y = y / x - x + x；
其他情况下，x △ y = y + y + x。
运算优先级：△ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 * 2 △ 6 △ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "120",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 * 2 △ 6 △ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nestin... |
logic-v2 | 定义 ◇，规则如下：
实数域上，x ◇ y = y * x + y。
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
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "54",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ◇ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth":... |
logic-v2 | 定义 ⊕，规则如下：
当x等于y时，x ⊕ y = (x + 2 - 4 + x) - y；
其他情况下，x ⊕ y = y - x * x + 5 - x。
和 ♡，规则如下：
当y是奇数时，x ♡ y = y - (x + 2 * x ⊕ y)；
其他情况下，x ♡ y = x ⊕ y + x + 3。
和 ⊗，规则如下：
当x是奇数时，x ⊗ y = x + y + 1 - y ⊕ y；
其他情况下，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: 4 ... | {
"game_data": {
"answer": "-2682",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ♡ 5 ⊕ 10 * 3 ⊗ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
... |
logic-v2 | Define ◎, the rules are as follows:
when x is greater than y, x ◎ y = y + x + x;
otherwise, x ◎ y = y * x + x.
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 expression inside th... | {
"game_data": {
"answer": "201.6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 * 5 □ 4 ◎ 5 ◎ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"... |
logic-v2 | Define ⊗, the rules are as follows:
when the sum of x and y is odd, x ⊗ y = y - x + y;
otherwise, x ⊗ y = y * x + x - x + 4.
and ☆, the rules are as follows:
on the real number field, x ☆ y = y / x * 3 - y ⊗ y.
and ⊙, the rules are as follows:
when x is a multiple of 5, x ⊙ y = y - x ☆ y;
otherwise, x ⊙ y = y... | {
"game_data": {
"answer": "-4588.34",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ☆ 9 ⊗ 5 ⊙ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"... |
logic-v2 | 定义 ☆，规则如下：
当x是奇数时，x ☆ y = x * x - x * y；
其他情况下，x ☆ y = abs(x * x) * 2 - y - x。
和 ⊕，规则如下：
实数域上，x ⊕ y = y + y * abs(y) ** y + x。
运算优先级：☆ = ⊕ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ☆ 5 / 3 ⊕ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-0.045977",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ☆ 5 / 3 ⊕ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"... |
logic-v2 | Define ◎, the rules are as follows:
when x is odd, x ◎ y = x * x + 5 - y;
otherwise, x ◎ y = x ** y * x.
and △, the rules are as follows:
on the real number field, x △ y = abs(y) * x.
and ♢, the rules are as follows:
when y is even, x ♢ y = (x * y) - y - 5;
otherwise, x ♢ y = y / (x * x).
The precedence of op... | {
"game_data": {
"answer": "52",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ◎ 4 △ 2",
"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 a multiple of 5, x ♢ y = y * y / x;
otherwise, x ♢ y = x + (y + y).
and ◎, the rules are as follows:
on the real number field, x ◎ y = y ♢ x.
and ◇, the rules are as follows:
when y is odd, x ◇ y = y - x / y;
otherwise, x ◇ y = y / x / y.
The precedence of operati... | {
"game_data": {
"answer": "27",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ◇ 3 ♢ 6 ◎ 1",
"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 = x * y ** y;
otherwise, x ⊙ y = y * y + x.
and ☆, the rules are as follows:
when x and y are both odd, x ☆ y = x / 3 ⊙ y;
otherwise, x ☆ y = x ⊙ (y - x).
and ⊗, the rules are as follows:
when x and y are both even, x ⊗ y = y * x;
other... | {
"game_data": {
"answer": "4.777778",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ☆ 2 * 6 / 2 ⊗ 10 ⊙ 4",
"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 ** (4 - y)。
和 ♢，规则如下：
当x是5的倍数时，x ♢ y = y + 4 - y + 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: 1 ◎ 4 ♢ 4 - 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ◎ 4 ♢ 4 - 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_... |
logic-v2 | 定义 ⊗，规则如下：
当x和y都是偶数时，x ⊗ y = y - x + y * x；
其他情况下，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: 8 * 6 ⊗ 2 + 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "66",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 * 6 ⊗ 2 + 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting... |
logic-v2 | 定义 ⊙，规则如下：
当x和y都是奇数时，x ⊙ y = y / x * x；
其他情况下，x ⊙ y = y - y * 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 = 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: 9 △ 10 ⊙ 1 ⊗ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "405",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 △ 10 ⊙ 1 ⊗ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesti... |
logic-v2 | 定义 ♢，规则如下：
实数域上，x ♢ y = 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 = 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 ○ 7 ♢ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-56.015625",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ○ 7 ♢ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nes... |
logic-v2 | 定义 ♡，规则如下：
实数域上，x ♡ y = 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: 9 ♡ 1 ○ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ♡ 1 ○ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dept... |
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: 2
Please fill your final ... | {
"game_data": {
"answer": "2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2",
"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 + y * x.
and ▽, the rules are as follows:
when y is a multiple of 5, x ▽ y = x * 3 * y;
otherwise, x ▽ y = (x * x) * y.
and ◎, the rules are as follows:
when y is odd, x ◎ y = y + y / x;
otherwise, x ◎ y = abs(x * x + y).
The precedence o... | {
"game_data": {
"answer": "2364",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ⊕ 8 ◎ 2 ▽ 10",
"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 = y + x - x。
和 ○，规则如下：
当x是3的倍数时，x ○ y = y - x / x；
其他情况下，x ○ y = (x + 4) + y * x。
和 ⊙，规则如下：
当y是偶数时，x ⊙ y = x / x + y * x；
其他情况下，x ⊙ y = x * x ○ y。
运算优先级：⊕ = ⊙ > ○ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 ⊙ 5 ○ 3 ⊕ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "4580",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ⊙ 5 ○ 3 ⊕ 10",
"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 + x + y.
and △, the rules are as follows:
on the real number field, x △ y = y ⊗ x + y + y.
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = (x ⊗ y) * x.
The precedence of operations: ⊗ > ** > * = / = % = ⊙ > + = - = △。
P... | {
"game_data": {
"answer": "264",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ⊙ 3 ** 1 △ 5 ⊗ 1",
"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 * x * y) + y + y.
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = y * (1 - y + y + x).
The precedence of operations: ⊙ > ◎ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parent... | {
"game_data": {
"answer": "63",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ⊙ 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 x is equal to y, x ♡ y = x * y + x;
otherwise, x ♡ y = abs(y / x).
and ◎, the rules are as follows:
on the real number field, x ◎ y = y + (x) * x.
The precedence of operations: ♡ > ** > * = / = % > + = - = ◎。
Parentheses have the highest priority, and the expression inside... | {
"game_data": {
"answer": "10",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ◎ 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 y is odd, x ◇ y = y - x + y;
otherwise, x ◇ y = x + x * y - x.
The precedence of operations: ◇ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 4 + 6 ... | {
"game_data": {
"answer": "44",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 + 6 ◇ 5 ◇ 10",
"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 + 2 + y / x.
and ◇, the rules are as follows:
on the real number field, x ◇ y = x / y □ y + x / y.
The precedence of operations: ◇ > ** > * = / = % > + = - = □。
Parentheses have the highest priority, and the expression inside the parentheses is... | {
"game_data": {
"answer": "10.617647",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ◇ 5 % 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 = y * x.
and ♢, the rules are as follows:
when the sum of x and y is odd, x ♢ y = y - x - x;
otherwise, x ♢ y = y * x + 1.
The precedence of operations: ♢ > ** = ♡ > * = / = % > + = -。
Parentheses have the highest priority, and the expression ins... | {
"game_data": {
"answer": "-3",
"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,
"nesting_dep... |
logic-v2 | Define ⊕, the rules are as follows:
when x is odd, x ⊕ y = x * y * x;
otherwise, x ⊕ y = y + x.
and ♢, the rules are as follows:
on the real number field, x ♢ y = abs(y) + x + x.
and ⊗, the rules are as follows:
when x is equal to y, x ⊗ y = y - x + x;
otherwise, x ⊗ y = 4 + y / x.
The precedence of operation... | {
"game_data": {
"answer": "5.875",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ⊗ 7 ⊕ 10 % 4 ♢ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
... |
logic-v2 | Define ○, the rules are as follows:
when the sum of x and y is even, x ○ y = y - y + x;
otherwise, x ○ y = 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 expr... | {
"game_data": {
"answer": "-18",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 * 6 ○ 9 ○ 10",
"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 a multiple of 3, x △ y = 1 - 2 + x * y * abs(x);
otherwise, x △ y = abs(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 t... | {
"game_data": {
"answer": "10",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 △ 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 x and y are both even, x ♡ y = 1 / y + x * x;
otherwise, x ♡ y = abs(y + x).
and □, the rules are as follows:
when x is a multiple of 3, x □ y = x - x * y;
otherwise, x □ y = (y + x ♡ y) / y.
The precedence of operations: ** = ♡ > * = / = % = □ > + = -。
Parentheses have ... | {
"game_data": {
"answer": "23.333333",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 □ 2 ♡ 1 * 5",
"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 / y.
and ○, the rules are as follows:
on the real number field, x ○ y = y * (y - x).
and ⊕, the rules are as follows:
on the real number field, x ⊕ y = 1 - y - x.
The precedence of operations: ⊗ > ** > * = / = % = ○ = ⊕ > + = -。
Parenthes... | {
"game_data": {
"answer": "108",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ⊗ 6 ⊕ 8 ○ 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 = y * x.
The precedence of operations: ** = ○ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 1 ○ 10 - 5 / 3
Please fill your fin... | {
"game_data": {
"answer": "8.333333",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ○ 10 - 5 / 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"... |
logic-v2 | 定义 ⊙，规则如下：
当y是偶数时，x ⊙ y = x - y / 3 - 3；
其他情况下，x ⊙ y = 5 - 4 - y * x。
和 ♡，规则如下：
当x是偶数时，x ♡ y = x - 4 + y - x；
其他情况下，x ♡ y = y + x * x * 2。
和 ○，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 ** 5 - 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: 7 ○ 3 ⊙ 4 ♡ 1
请将最终答案填入... | {
"game_data": {
"answer": "1859.034937",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ○ 3 ⊙ 4 ♡ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
... |
logic-v2 | Define ○, the rules are as follows:
when y is odd, x ○ y = y * x;
otherwise, x ○ y = x * y - x.
The precedence of operations: ** = ○ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 4 ○ 1
Please f... | {
"game_data": {
"answer": "4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ○ 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 = x - y / 3 - y。
和 ☆，规则如下：
实数域上，x ☆ y = y + (x) ⊙ 2。
和 ♢，规则如下：
实数域上，x ♢ y = x + y - x。
运算优先级：⊙ > ☆ > ** > * = / = % = ♢ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 ⊙ 7 ♢ 9 ☆ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "13.333333",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ⊙ 7 ♢ 9 ☆ 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 is even, x △ y = y + y - x;
otherwise, x △ y = y + y - (x).
The precedence of operations: △ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 7
Pleas... | {
"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 | Define ⊙, the rules are as follows:
when y is even, x ⊙ y = 4 + y + x;
otherwise, x ⊙ y = y * 2 + x - x.
and ♢, the rules are as follows:
when y is a multiple of 5, x ♢ y = (4 - x / x * y);
otherwise, x ♢ y = y + x * y ⊙ y.
and ⊕, the rules are as follows:
on the real number field, x ⊕ y = y / abs(x + y) * 1.... | {
"game_data": {
"answer": "18",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ⊕ 4 ⊙ 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 x is odd, x ◎ y = x * y + 3;
otherwise, x ◎ y = x * y.
and ⊙, the rules are as follows:
when the sum of x and y is odd, x ⊙ y = x + (y ◎ x);
otherwise, x ⊙ y = x + (y).
The precedence of operations: ◎ > ⊙ > ** > * = / = % > + = -。
Parentheses have the highest priority, a... | {
"game_data": {
"answer": "85",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 + 8 ⊙ 3 ◎ 2",
"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 - 4 - 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: 6
Please fill your fina... | {
"game_data": {
"answer": "6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null... |
logic-v2 | Define ◎, the rules are as follows:
on the real number field, x ◎ y = y + y - x / y * y.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = x / y ◎ y + y - x.
The precedence of operations: ◎ = ⊗ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parenthese... | {
"game_data": {
"answer": "17",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ⊗ 2 ◎ 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：
当x是3的倍数时，x ☆ y = 3 - (x + 5 + x + y)；
其他情况下，x ☆ y = x + 5 / y。
和 ◎，规则如下：
实数域上，x ◎ y = x * (y * x) * 4。
运算优先级：☆ = ◎ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 ◎ 1 ☆ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "16.555556",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ◎ 1 ☆ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nest... |
logic-v2 | 定义 ⊙，规则如下：
实数域上，x ⊙ y = x + y - y。
和 ☆，规则如下：
实数域上，x ☆ y = y ⊙ x。
和 ○，规则如下：
当x是偶数时，x ○ y = x ☆ y - 1；
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 ○ 10 ☆ 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 ○ 10 ☆ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dep... |
logic-v2 | Define ○, the rules are as follows:
when x is even, x ○ y = x * 3 - x / y;
otherwise, x ○ y = x * y + y.
The precedence of operations: ** > * = / = % = ○ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 7 ○ 5... | {
"game_data": {
"answer": "40",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ○ 5 * 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：
实数域上，x ◎ y = y * x * 2 - x。
和 ◇，规则如下：
当y是偶数时，x ◇ y = x + x * abs(y + 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: 3 ◎ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "27",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ◎ 5",
"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 = abs(y + x * x).
and ▽, the rules are as follows:
on the real number field, x ▽ y = y + x - y.
and ♢, the rules are as follows:
when the sum of x and y is odd, x ♢ y = x - y + x;
otherwise, x ♢ y = y * x.
The precedence of operations: ♢ > ** =... | {
"game_data": {
"answer": "84",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ⊙ 3 ▽ 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 = abs(y + x - x + y) ** x;
otherwise, x ⊕ y = (2) - x + y * 1 - x.
and ⊙, the rules are as follows:
when x is a multiple of 5, x ⊙ y = x + y - x * y;
otherwise, x ⊙ y = 4 - y / 1 ⊕ x.
and ♡, the rules are as follows:
when x is equal to y, x ♡ y = x + x ... | {
"game_data": {
"answer": "17",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ⊙ 4 ♡ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dep... |
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