env stringclasses 1
value | prompt stringlengths 119 673 | extra dict |
|---|---|---|
logic-v2 | Define ○, the rules are as follows:
on the real number field, x ○ y = y - x * x.
The precedence of operations: ** = ○ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 6 ○ 2 ○ 8
Please fill your fina... | {
"game_data": {
"answer": "-1148",
"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_... |
logic-v2 | Define ♡, the rules are as follows:
when x is equal to y, x ♡ y = y - y ** y - x;
otherwise, x ♡ y = y + x.
and ⊕, the rules are as follows:
on the real number field, x ⊕ y = y + x + abs(y * x).
The precedence of operations: ** = ⊕ > * = / = % > + = - = ♡。
Parentheses have the highest priority, and the expression... | {
"game_data": {
"answer": "10",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ⊕ 1 ♡ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dep... |
logic-v2 | 定义 ▽，规则如下：
当x和y都是偶数时，x ▽ y = 1 / x * 3 / y ** 2；
其他情况下，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: 4 / 10 ▽ 8 ▽ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-0.502651",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 / 10 ▽ 8 ▽ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
... |
logic-v2 | 定义 ○，规则如下：
实数域上，x ○ y = 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 ○ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ○ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": ... |
logic-v2 | Define △, the rules are as follows:
on the real number field, x △ y = y + x / x.
The precedence of operations: ** = △ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 5 △ 6 △ 3
Please fill your fina... | {
"game_data": {
"answer": "4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 △ 6 △ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dept... |
logic-v2 | 定义 ☆，规则如下：
实数域上，x ☆ y = 1 * x * 5 / y。
和 ▽，规则如下：
当x小于y时，x ▽ y = y + x + y ☆ x；
其他情况下，x ▽ y = 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: 9 ▽ 9 ☆ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ▽ 9 ☆ 5",
"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 * 1 + y;
otherwise, x ♢ y = x - y - y.
and ◇, the rules are as follows:
when y is odd, x ◇ y = x ♢ x - y;
otherwise, x ◇ y = y ♢ (x * y + x).
and ⊗, the rules are as follows:
when x is a multiple of 5, x ⊗ y = x ◇ y - x + x;
otherwise, x ⊗ y = x ... | {
"game_data": {
"answer": "44",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ◇ 6 ♢ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_de... |
logic-v2 | 定义 ☆，规则如下：
实数域上，x ☆ y = x * y * x。
和 ◇，规则如下：
当y是奇数时，x ◇ y = y + x / x；
其他情况下，x ◇ y = y ** x - y。
运算优先级：◇ > ** = ☆ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 ☆ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "64",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ☆ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth":... |
logic-v2 | Define ⊕, the rules are as follows:
on the real number field, x ⊕ y = x - y + y - x - x.
and ▽, the rules are as follows:
on the real number field, x ▽ y = y ⊕ x * 4 - y.
and ⊗, the rules are as follows:
when x and y are both even, x ⊗ y = x + y * 1 - y * x;
otherwise, x ⊗ y = x - x * y + 2 * y.
The precedence ... | {
"game_data": {
"answer": "-10",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ⊕ 1 ▽ 2 ⊗ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nestin... |
logic-v2 | Define ◇, the rules are as follows:
on the real number field, x ◇ y = x * x / 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 an... | {
"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 = 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: 5 ▽ 7 * 7 - 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "36.2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ▽ 7 * 7 - 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesti... |
logic-v2 | Define ▽, the rules are as follows:
when x is greater than y, x ▽ y = x - y - x;
otherwise, x ▽ y = x + x / y.
The precedence of operations: ** > * = / = % = ▽ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression:... | {
"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 | 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: 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "7",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | 定义 ◎，规则如下：
实数域上，x ◎ y = (x - y * x + 5)。
和 △，规则如下：
当y是偶数时，x △ y = y + y - x；
其他情况下，x △ y = 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 ◎ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-51",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ◎ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth"... |
logic-v2 | 定义 ▽，规则如下：
实数域上，x ▽ y = y * x。
运算优先级：▽ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1",
"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 * 3 * x * y.
and □, the rules are as follows:
when the sum of x and y is even, x □ y = x ** x + y;
otherwise, x □ y = x ⊕ x - x / y.
and ☆, the rules are as follows:
on the real number field, x ☆ y = y * x ⊕ 1.
The precedence of operations:... | {
"game_data": {
"answer": "0.002074",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 / 1 ☆ 10 □ 3 ⊕ 4",
"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 + y / x + y.
and ○, the rules are as follows:
when y is a multiple of 5, x ○ y = x + y + y - y;
otherwise, x ○ y = y + abs(x * 3 / x).
The precedence of operations: ** = ◎ = ○ > * = / = % > + = -。
Parentheses have the highest priority, and th... | {
"game_data": {
"answer": "7",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ○ 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 / abs(x) * y.
and ○, the rules are as follows:
on the real number field, x ○ y = (3 ⊙ y) * x.
and ⊕, the rules are as follows:
on the real number field, x ⊕ y = (1 - x * y).
The precedence of operations: ⊕ > ** > * = / = % = ⊙ = ○ > + = -。
Pa... | {
"game_data": {
"answer": "4.226682",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 + 7 ○ 3 ⊕ 4 ⊙ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
... |
logic-v2 | Define ○, the rules are as follows:
when x is less than y, x ○ y = (x / 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 expression: ... | {
"game_data": {
"answer": "-6.222222",
"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_... |
logic-v2 | 定义 ⊙，规则如下：
当y是3的倍数时，x ⊙ y = x - x + abs(y * y - y)；
其他情况下，x ⊙ y = x / 2 - y + 3。
和 ♢，规则如下：
当y是偶数时，x ♢ y = x + x + y；
其他情况下，x ♢ y = x + abs(x) * y + x + x。
和 ♡，规则如下：
当x是偶数时，x ♡ y = y / x + 3 ⊙ 3 ** 5；
其他情况下，x ♡ y = y ** 2 - 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: ... | {
"game_data": {
"answer": "72",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ♢ 7 ♡ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dep... |
logic-v2 | 定义 ⊕，规则如下：
实数域上，x ⊕ y = x * y。
和 ▽，规则如下：
实数域上，x ▽ y = x * x ⊕ y。
和 ☆，规则如下：
实数域上，x ☆ y = y ▽ 4 - x。
运算优先级：▽ > ⊕ > ** > * = / = % > + = - = ☆。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 ☆ 1 ⊕ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "58",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ☆ 1 ⊕ 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 = abs(y) - x * x + y.
and ◎, the rules are as follows:
when y is a multiple of 3, x ◎ y = y + y ▽ 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: ○ > *... | {
"game_data": {
"answer": "7",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ▽ 4 ○ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dep... |
logic-v2 | Define ⊙, the rules are as follows:
on the real number field, x ⊙ y = x - y - 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 * x.
The precedence of operations: ○ > ** = ◇ > * = / = % = ⊙ > + = -。
Parentheses hav... | {
"game_data": {
"answer": "194",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ○ 10 ⊙ 10 ◇ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nest... |
logic-v2 | 定义 ○，规则如下：
当x和y的和是奇数时，x ○ y = x - y + x；
其他情况下，x ○ y = 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: 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | 定义 △，规则如下：
当x和y的和是奇数时，x △ y = x / (y - x)；
其他情况下，x △ y = abs(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 ** 10 △ 1 % 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0.099213",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ** 10 △ 1 % 10",
"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 = y - x + x.
and □, the rules are as follows:
on the real number field, x □ y = x + y ☆ 4 / x.
The precedence of operations: ☆ > ** > * = / = % > + = - = □。
Parentheses have the highest priority, and the expression inside the parentheses is calcula... | {
"game_data": {
"answer": "5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 □ 10",
"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 = x / y - x - y / x；
其他情况下，x △ y = x / 2 * x * y - y。
运算优先级：** = △ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 △ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "186",
"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：
实数域上，x ○ y = y / x - x + y + x。
运算优先级：** = ○ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5 ○ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "3.6",
"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 y is even, x △ y = (5 + x / y ** 5);
otherwise, x △ y = (y + x) - y + x.
The precedence of operations: ** > * = / = % = △ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expressi... | {
"game_data": {
"answer": "0.444444",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 / 9 △ 5",
"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 - y).
and ♡, the rules are as follows:
on the real number field, x ♡ y = y * x * x.
The precedence of operations: ◎ > ** > * = / = % = ♡ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculate... | {
"game_data": {
"answer": "5184",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ◎ 5 * 4 ♡ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesti... |
logic-v2 | Define ☆, the rules are as follows:
when x is a multiple of 3, x ☆ y = (x * x * y);
otherwise, x ☆ y = 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 expression inside... | {
"game_data": {
"answer": "8.1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ☆ 2 ☆ 10 ◇ 1",
"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 = y + x * y - 3。
和 ☆，规则如下：
当y是3的倍数时，x ☆ y = x + 2 ⊕ y * x；
其他情况下，x ☆ y = y * x - x。
和 ⊗，规则如下：
当x和y都是奇数时，x ⊗ y = x + x + y - y；
其他情况下，x ⊗ y = abs(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: 7 ⊕ 4 ⊗ 3 ☆ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "2333",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ⊕ 4 ⊗ 3 ☆ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesti... |
logic-v2 | Define ◇, the rules are as follows:
when x is equal to y, x ◇ y = abs(y + x) * x * x;
otherwise, x ◇ y = 5 - 2 ** 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": "0.06",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 * 3 / 5 ◇ 5",
"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 + 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 △ 9
Please fill your final an... | {
"game_data": {
"answer": "27",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 △ 9",
"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 - x + 2。
和 ▽，规则如下：
实数域上，x ▽ y = y + x ☆ x。
运算优先级：▽ > ** > * = / = % > + = - = ☆。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 ▽ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ▽ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth":... |
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 = (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: 9 ○ 9 ⊙ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1701",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ○ 9 ⊙ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_d... |
logic-v2 | Define ◎, the rules are as follows:
on the real number field, x ◎ y = x * y + y.
and ▽, the rules are as follows:
on the real number field, x ▽ y = (y) + x.
The precedence of operations: ▽ > ** = ◎ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated fi... | {
"game_data": {
"answer": "17",
"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 y is odd, x ◎ y = x * x + y - y;
otherwise, x ◎ y = y + x - x - 5 + y.
and ⊕, the rules are as follows:
when y is odd, x ⊕ y = abs(x - x * y);
otherwise, x ⊕ y = 1 + x - y * x ◎ x.
The precedence of operations: ⊕ > ** > * = / = % > + = - = ◎。
Parentheses have the highest... | {
"game_data": {
"answer": "-61",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ◎ 9 ⊕ 1 - 7 * 8",
"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 = y + x - y / x.
and ♢, the rules are as follows:
when y is odd, x ♢ y = x - x - x ♡ y;
otherwise, x ♢ y = y ♡ 4 * y - x.
The precedence of operations: ♢ > ** > * = / = % = ♡ > + = -。
Parentheses have the highest priority, and the expression insi... | {
"game_data": {
"answer": "5.302198",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ♢ 3 ♡ 2 ♡ 3",
"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 = y - (x * y)；
其他情况下，x ▽ y = y * x + x。
运算优先级：** = ▽ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 - 3 ▽ 9 - 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-37",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 - 3 ▽ 9 - 9",
"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 = x * y + (y)。
运算优先级：** = ◇ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 9 ◇ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "90",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ◇ 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 = y / x;
otherwise, x ▽ y = y - 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 expression: 9... | {
"game_data": {
"answer": "9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ▽ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": ... |
logic-v2 | Define ○, the rules are as follows:
on the real number field, x ○ y = 1 / x + y.
The precedence of operations: ** = ○ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 5 ○ 6 - 2 - 1
Please fill your ... | {
"game_data": {
"answer": "3.2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ○ 6 - 2 - 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nestin... |
logic-v2 | 定义 ☆，规则如下：
实数域上，x ☆ y = y + y ** 1 * x。
和 △，规则如下：
当x大于y时，x △ y = y + (x + x) / x；
其他情况下，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: 1 ☆ 4 % 6 △ 9 ** 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ☆ 4 % 6 △ 9 ** 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nes... |
logic-v2 | 定义 ⊗，规则如下：
实数域上，x ⊗ y = (y ** x)。
和 ○，规则如下：
当x和y的和是奇数时，x ○ y = 5 + 5 ⊗ y * x；
其他情况下，x ○ y = 1 + x + y - y。
和 ☆，规则如下：
实数域上，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: 7 ○ 2 ⊗ 4 ☆ 1 ⊗ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "10",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ○ 2 ⊗ 4 ☆ 1 ⊗ 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 = y * y - x.
and ⊕, the rules are as follows:
on the real number field, x ⊕ y = x * y.
and ♡, the rules are as follows:
on the real number field, x ♡ y = (y ⊕ x).
The precedence of operations: ⊗ > ** = ⊕ = ♡ > * = / = % > + = -。
Parentheses have ... | {
"game_data": {
"answer": "176",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ♡ 2 ⊕ 5 ⊗ 7",
"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3的倍数时，x ♢ y = y * y / x；
其他情况下，x ♢ y = y * x + 2。
和 ⊗，规则如下：
实数域上，x ⊗ y = (y / x * x)。
运算优先级：** > * = / = % = ⊗ > + = - = ♢。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7 ♢ 8 + 5 ⊗ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "63",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ♢ 8 + 5 ⊗ 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 = x - y * y * x。
运算优先级：** = ◇ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 ◇ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-320",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ◇ 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 y is even, x ⊕ y = x + y;
otherwise, x ⊕ y = 3 - 4 - y - y * x.
and ♢, 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 odd, x ⊗ y = y - y + 1 - x ♢ y;
otherwise, x ⊗ y = abs(y - x + y + y).
The... | {
"game_data": {
"answer": "-990",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ⊗ 8 ♢ 3 ⊕ 1 ♢ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"n... |
logic-v2 | 定义 □，规则如下：
实数域上，x □ y = x ** 4 * abs(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 □ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "32768",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 □ 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y是5的倍数时，x ◎ y = abs(x - 2 * x) + y；
其他情况下，x ◎ y = y * 5 / 1 - x。
和 ◇，规则如下：
当x是3的倍数时，x ◇ y = (x ◎ 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: 1 ◇ 3 ◎ 4 / 9 ** 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-0.999661",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ◇ 3 ◎ 4 / 9 ** 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
... |
logic-v2 | 定义 ⊗，规则如下：
当x和y的和是偶数时，x ⊗ y = (x + y) * y；
其他情况下，x ⊗ y = x / 4 + abs(y)。
和 ◎，规则如下：
当y是3的倍数时，x ◎ y = (x ⊗ x) + y；
其他情况下，x ◎ y = x ⊗ y。
和 ⊕，规则如下：
当y是偶数时，x ⊕ y = y + x；
其他情况下，x ⊕ y = y ** x * x。
运算优先级：⊕ > ** = ◎ > * = / = % = ⊗ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7 ⊗ 9 ⊕ 8 ◎ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "19.75",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ⊗ 9 ⊕ 8 ◎ 1",
"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 = (y - y) - 2 * 4 - x.
and ▽, the rules are as follows:
on the real number field, x ▽ y = 5 - x * 2 / y + 1.
and ○, the rules are as follows:
on the real number field, x ○ y = y * y + x + x ▽ x.
The precedence of operations: ⊗ > ○ > ** > * = / = ... | {
"game_data": {
"answer": "11.647059",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ○ 6 ▽ 9 ⊗ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"... |
logic-v2 | 定义 ▽，规则如下：
实数域上，x ▽ y = (x) * x + y。
运算优先级：** > * = / = % > + = - = ▽。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6
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:
on the real number field, x ○ y = x ** x - y - y.
The precedence of operations: ** > * = / = % > + = - = ○。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 1
Please fill your final a... | {
"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:
when x is a multiple of 5, x □ y = y * (y) + x;
otherwise, x □ y = (y + x).
The precedence of operations: □ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression... | {
"game_data": {
"answer": "19",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 □ 1 □ 2 □ 6",
"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 - 2 - x / y。
和 ○，规则如下：
当x和y的和是奇数时，x ○ y = y ♡ x；
其他情况下，x ○ y = 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: 5 + 6 ○ 4 - 3 ♡ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "6.041667",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 + 6 ○ 4 - 3 ♡ 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5的倍数时，x ◎ y = y + 3 * x - y；
其他情况下，x ◎ y = x * 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: 6 ○ 4 ◎ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "3142",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ○ 4 ◎ 10",
"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是奇数时，x ○ y = y + 3 + (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: 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",
"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和y都是奇数时，x ⊙ y = y / x；
其他情况下，x ⊙ y = x / y - y。
和 ☆，规则如下：
当x是偶数时，x ☆ y = 2 ⊙ y * x；
其他情况下，x ☆ y = x * y - y。
和 ◇，规则如下：
实数域上，x ◇ y = x - y - abs(y)。
运算优先级：⊙ = ◇ > ☆ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ◇ 9 - 7 ☆ 2 ⊙ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "41.8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ◇ 9 - 7 ☆ 2 ⊙ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"... |
logic-v2 | 定义 ▽，规则如下：
实数域上，x ▽ y = y + 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 ▽ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "70",
"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_dep... |
logic-v2 | 定义 □，规则如下：
当x大于y时，x □ y = 5 - y - x；
其他情况下，x □ y = x + 4 * (x / y)。
和 ⊗，规则如下：
实数域上，x ⊗ y = x + (y) * y □ x。
运算优先级：□ > ** > * = / = % > + = - = ⊗。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5 ⊗ 3 □ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "6.8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ⊗ 3 □ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_de... |
logic-v2 | Define □, the rules are as follows:
when the sum of x and y is odd, x □ y = x * x * y;
otherwise, x □ y = x * abs(y).
and ⊕, the rules are as follows:
when the sum of x and y is odd, x ⊕ y = x - y * y ** y;
otherwise, x ⊕ y = y + y - x.
The precedence of operations: □ = ⊕ > ** > * = / = % > + = -。
Parentheses h... | {
"game_data": {
"answer": "-56",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 □ 10 ⊕ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_d... |
logic-v2 | Define ○, the rules are as follows:
on the real number field, x ○ y = y * y * y + x.
The precedence of operations: ** > * = / = % = ○ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 3 ○ 4 * 10 - 9
Please fill ... | {
"game_data": {
"answer": "661",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ○ 4 * 10 - 9",
"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 = y + x - y + y。
和 ▽，规则如下：
实数域上，x ▽ y = x * y + 1。
运算优先级：▽ > ** = ◎ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 ▽ 7 ◎ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "66",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ▽ 7 ◎ 9",
"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 = abs(x * x) + 1 + y.
and ☆, the rules are as follows:
when y is a multiple of 5, x ☆ y = x * x * x * y;
otherwise, x ☆ y = abs(y + x ** y).
The precedence of operations: ☆ > ** > * = / = % > + = - = ♡。
Parentheses have the highest priority, and ... | {
"game_data": {
"answer": "6",
"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:
when x and y are both odd, x ☆ y = 5 + abs(y * x - x);
otherwise, x ☆ y = x * y ** 2 - y.
and ◎, the rules are as follows:
when x is a multiple of 5, x ◎ y = x * y;
otherwise, x ◎ y = y / x.
The precedence of operations: ** > * = / = % = ☆ = ◎ > + = -。
Parentheses have the hi... | {
"game_data": {
"answer": "32391",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 * 4 ◎ 10 ☆ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"ne... |
logic-v2 | 定义 △，规则如下：
实数域上，x △ y = 1 - x * y + y。
运算优先级：** = △ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "7",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | 定义 ⊙，规则如下：
实数域上，x ⊙ y = y - y / x + 1。
和 ⊕，规则如下：
当x是3的倍数时，x ⊕ y = x - 2 * y * 4 + x；
其他情况下，x ⊕ y = x * y。
和 ○，规则如下：
当y是5的倍数时，x ○ y = y ⊕ x + y；
其他情况下，x ○ y = y * (x)。
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 ○ 8 ⊕ 6 ⊙ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0.091667",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 / 5 ○ 8 ⊕ 6 ⊙ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
... |
logic-v2 | 定义 ♡，规则如下：
当x等于y时，x ♡ y = 4 * x - x ** y；
其他情况下，x ♡ y = x * y + 3 - y。
和 ♢，规则如下：
当x是偶数时，x ♢ y = x - (2 * 5) ♡ y；
其他情况下，x ♢ y = y + x / y * y。
运算优先级：♢ > ♡ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 ♢ 2 - 4 ♡ 3 % 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-14",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ♢ 2 - 4 ♡ 3 % 9",
"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 = y * x。
和 ⊕，规则如下：
实数域上，x ⊕ y = x + y。
运算优先级：♡ > ** = ⊕ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 ⊕ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "16",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ⊕ 8",
"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 = x + x - y / 5.
The precedence of operations: ◇ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expre... | {
"game_data": {
"answer": "10",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": nu... |
logic-v2 | Define ♢, the rules are as follows:
on the real number field, x ♢ y = y + y + x - x.
and □, the rules are as follows:
when x is odd, x □ y = x * x - y * x;
otherwise, x □ y = x * y + x.
and ⊗, the rules are as follows:
when x is equal to y, x ⊗ y = y - y * x □ 1;
otherwise, x ⊗ y = abs(x + y).
The precedence ... | {
"game_data": {
"answer": "120",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ** 7 ♢ 10 □ 2 ⊗ 3",
"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 odd, x ⊗ y = y - x / y - y;
otherwise, x ⊗ y = y / y * abs(y) * x.
and ⊙, the rules are as follows:
when x is even, x ⊙ y = y + x + y ⊗ x;
otherwise, x ⊙ y = x / y * y.
and ◇, the rules are as follows:
on the real number field, x ◇ y = x * x + y.
The precedence of... | {
"game_data": {
"answer": "3849",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ⊙ 8 ◇ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_d... |
logic-v2 | 定义 ⊕，规则如下：
当x是偶数时，x ⊕ y = y - y - x；
其他情况下，x ⊕ y = x - y - y。
和 ☆，规则如下：
当x是奇数时，x ☆ y = x ⊕ x * y；
其他情况下，x ☆ y = y - x ⊕ y。
和 ◇，规则如下：
当y是偶数时，x ◇ y = x + y / x；
其他情况下，x ◇ y = y - y * x。
运算优先级：⊕ > ☆ > ** > * = / = % > + = - = ◇。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 ⊕ 9 ◇ 1 ☆ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-11",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ⊕ 9 ◇ 1 ☆ 1",
"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: 6 + 7 ◇ 6 % 9
Please fill y... | {
"game_data": {
"answer": "8.142857",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 + 7 ◇ 6 % 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"n... |
logic-v2 | Define ⊗, the rules are as follows:
when x is odd, x ⊗ y = x - y - abs(x) * x + 1;
otherwise, x ⊗ y = x - x + y - x + x.
and ♢, the rules are as follows:
when x is greater than y, x ♢ y = x + y * y + x / x;
otherwise, x ♢ y = 4 / y - x + 3 - 2.
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = ... | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ⊙ 2 ⊗ 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和y的和是偶数时，x ○ y = x * y；
其他情况下，x ○ y = y - 3 * x。
运算优先级：○ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7 ○ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-15",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ○ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth"... |
logic-v2 | 定义 ♢，规则如下：
实数域上，x ♢ y = y * x。
和 ◎，规则如下：
当y是偶数时，x ◎ y = x + y + 3 + y；
其他情况下，x ◎ y = x * x ** y + x。
和 ♡，规则如下：
当x大于y时，x ♡ y = x ♢ y + x * x + y；
其他情况下，x ♡ y = x - x - x ♢ y。
运算优先级：♢ = ♡ > ** > * = / = % = ◎ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ♡ 7 ◎ 6 ♢ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "80",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ♡ 7 ◎ 6 ♢ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting... |
logic-v2 | 定义 ☆，规则如下：
实数域上，x ☆ y = x - y + x / x - y。
和 □，规则如下：
当x大于y时，x □ y = x + 2 ☆ y + y - y；
其他情况下，x □ y = y + y - x + (2)。
运算优先级：□ > ** > * = / = % = ☆ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 ☆ 5 % 3 - 9 □ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ☆ 5 % 3 - 9 □ 6",
"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是奇数时，x ⊕ y = 3 - 5 - y - x；
其他情况下，x ⊕ y = x - x * x + (y) - 3。
和 △，规则如下：
当x大于y时，x △ y = y ⊕ y - x * x * y；
其他情况下，x △ y = x / y - 3。
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: 6 △ 8 ♡ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "7.222222",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 △ 8 ♡ 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y是奇数时，x ▽ y = y / y - x * x；
其他情况下，x ▽ y = y - x * x - x。
运算优先级：▽ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7 ▽ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-48",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ▽ 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 is odd, x △ y = y * 1 + abs(4 + x);
otherwise, x △ y = x * y * y - x + x.
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 = x * x - x * abs(y - y).
The precedence of oper... | {
"game_data": {
"answer": "156.25",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ♢ 1 △ 5 ○ 10",
"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 = x - y - x - 1。
和 ◇，规则如下：
实数域上，x ◇ y = x ⊙ y - y + x + 5。
和 □，规则如下：
实数域上，x □ y = 5 * 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: 4 ⊙ 3 □ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-47",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ⊙ 3 □ 9",
"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 / 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 ▽ 3
Please fill your final an... | {
"game_data": {
"answer": "0.333333",
"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_d... |
logic-v2 | 定义 ⊗，规则如下：
实数域上，x ⊗ y = y * x + (y - x)。
和 ♡，规则如下：
实数域上，x ♡ y = x * y ⊗ y ** y。
和 ◎，规则如下：
实数域上，x ◎ y = y * (x) + 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 ◎ 5 ⊗ 10 ♡ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "16953",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ◎ 5 ⊗ 10 ♡ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nes... |
logic-v2 | Define ♢, the rules are as follows:
on the real number field, x ♢ y = x - y + y / x.
and ○, the rules are as follows:
when y is odd, x ○ y = (3) * x - y - 1;
otherwise, x ○ y = y - y - x.
and ◇, the rules are as follows:
on the real number field, x ◇ y = y - y + x.
The precedence of operations: ○ > ◇ > ** > * =... | {
"game_data": {
"answer": "12.818182",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ◇ 3 + 5 % 2 ♢ 2 ○ 4",
"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 3, x ▽ y = x * y ** y - y + x;
otherwise, x ▽ y = x ** y - x * 1 * y.
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": "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 | 定义 ♡，规则如下：
当x大于y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 = 5 ** 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
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ♡ 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 and y are both odd, x ◇ y = 2 + 2 + y + y + x;
otherwise, x ◇ y = x / y - (y ** 4).
The precedence of operations: ◇ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of... | {
"game_data": {
"answer": "-6566.111111",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ◇ 9 - 6 % 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
... |
logic-v2 | Define ◎, the rules are as follows:
on the real number field, x ◎ y = x - x - y.
and ⊗, the rules are as follows:
when x is less than y, x ⊗ y = y + x;
otherwise, x ⊗ y = (x ◎ 5 + y).
The precedence of operations: ** > * = / = % = ⊗ > + = - = ◎。
Parentheses have the highest priority, and the expression inside the... | {
"game_data": {
"answer": "-2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ◎ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth":... |
logic-v2 | Define ⊙, the rules are as follows:
on the real number field, x ⊙ y = y - y + 1 - x.
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 = (x * y) * 5 - x.
The precedence of operations: ⊙ > ** = ▽ = ☆ > * = / = % > + ... | {
"game_data": {
"answer": "0",
"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_dept... |
logic-v2 | Define ⊕, the rules are as follows:
when y is even, x ⊕ y = 2 + abs(x / 1) - y * y;
otherwise, x ⊕ y = y - abs(y) - x - x + x.
and ♢, the rules are as follows:
when the sum of x and y is even, x ♢ y = y ** x;
otherwise, x ♢ y = y + x - y ⊕ y - y.
and ⊗, the rules are as follows:
when y is a multiple of 5, x ⊗ y... | {
"game_data": {
"answer": "48.481481",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ⊕ 6 ⊗ 2 ♢ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"... |
logic-v2 | 定义 ▽，规则如下：
当x等于y时，x ▽ y = y + y - x；
其他情况下，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 ▽ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ▽ 2",
"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 = (y + x) * 1.
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 calculated fi... | {
"game_data": {
"answer": "16",
"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:
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: 7 ▽ 1
Please fill your fin... | {
"game_data": {
"answer": "-6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ▽ 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 = 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 ◇ 2 + 2 - 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ◇ 2 + 2 - 7",
"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 - (y / y ** x)。
和 ⊕，规则如下：
当x大于y时，x ⊕ y = x + y - 2 + 4；
其他情况下，x ⊕ y = x - x + x + y。
和 ⊗，规则如下：
实数域上，x ⊗ y = x + x ⊕ y。
运算优先级：⊙ > ⊕ = ⊗ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 ⊗ 8 ⊙ 10 ⊕ 5 % 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "3.0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ⊗ 8 ⊙ 10 ⊕ 5 % 4",
"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小于y时，x ◇ y = y + 4 + x + y - 2；
其他情况下，x ◇ y = y + y + x + 1。
运算优先级：◇ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | Define □, the rules are as follows:
when y is odd, x □ y = y * x - y / y * x;
otherwise, x □ y = y / x * x - x * x.
and ♡, the rules are as follows:
when x is odd, x ♡ y = x - 4 + y * x - y;
otherwise, x ♡ y = x / y / x - 2 □ 1.
and △, the rules are as follows:
on the real number field, x △ y = y / x □ y * y.... | {
"game_data": {
"answer": "-63.875",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 □ 6 ♡ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nestin... |
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