env stringclasses 1
value | prompt stringlengths 119 673 | extra dict |
|---|---|---|
logic-v2 | 定义 ▽，规则如下：
当x和y都是奇数时，x ▽ y = abs(y + x + y - y ** x)；
其他情况下，x ▽ y = y - x - x * x。
运算优先级：** > * = / = % = ▽ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 / 7 ▽ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "4.387755",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 / 7 ▽ 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大于y时，x ♢ y = y * x - y - y + x；
其他情况下，x ♢ y = 5 - y - x - 1 - x。
和 ⊕，规则如下：
实数域上，x ⊕ y = abs(y * x) + y - y ** x。
和 ⊙，规则如下：
实数域上，x ⊙ y = y - 5 / 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 ♢ 7 ⊙ 5 ⊕ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "32721.989848",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ♢ 7 ⊙ 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5的倍数时，x △ y = y / 4 / x - y；
其他情况下，x △ y = y + y * 5 + x。
运算优先级：** > * = / = % = △ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 △ 9 + 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "67",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 △ 9 + 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 = x * x - y - y.
and ▽, the rules are as follows:
on the real number field, x ▽ y = x - x ⊗ y - 2.
and ◇, the rules are as follows:
on the real number field, x ◇ y = y ⊗ x - 5.
The precedence of operations: ◇ > ⊗ > ** > * = / = % > + = - = ▽。
Par... | {
"game_data": {
"answer": "-12210",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ◇ 2 ⊗ 5 ▽ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nes... |
logic-v2 | Define ⊙, the rules are as follows:
on the real number field, x ⊙ y = y + 4 + 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 = y / x / x + x.
The precedence of operations: ⊙ > ** > * = / = % > + = - = ○ = △。... | {
"game_data": {
"answer": "35.4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 △ 9 ⊙ 10 ○ 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 a multiple of 5, x ♡ y = 5 * y ** x;
otherwise, x ♡ y = abs(x / y - y).
and □, the rules are as follows:
on the real number field, x □ y = 4 + abs(x + y).
The precedence of operations: ♡ > ** = □ > * = / = % > + = -。
Parentheses have the highest priority, and the expr... | {
"game_data": {
"answer": "20.25",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ♡ 8 □ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_... |
logic-v2 | 定义 ♡，规则如下：
实数域上，x ♡ y = x - y + x + 1。
和 ⊕，规则如下：
实数域上，x ⊕ y = x * y ♡ y + 5。
运算优先级：♡ > ** = ⊕ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ⊕ 2 + 8 ♡ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "18",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ⊕ 2 + 8 ♡ 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 - 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: 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 | Define ▽, the rules are as follows:
on the real number field, x ▽ y = abs(y + x) - x.
The precedence of operations: ** > * = / = % > + = - = ▽。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 3 ▽ 2 - 8
Please fill your... | {
"game_data": {
"answer": "-6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ▽ 2 - 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dep... |
logic-v2 | Define ○, the rules are as follows:
when the sum of x and y is odd, x ○ y = x + abs(5 / 2) + y * 4;
otherwise, x ○ y = x + x - y + y.
and ⊕, the rules are as follows:
on the real number field, x ⊕ y = x / x * y * y ○ x.
and ◇, the rules are as follows:
when y is a multiple of 5, x ◇ y = y * x + y + x + y;
other... | {
"game_data": {
"answer": "98",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ◇ 5 ○ 2 ⊕ 7",
"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 + 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 fina... | {
"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 + 3 - abs(y * x)。
和 ⊕，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。
运算优先级：◇ > ** = ⊕ > * = / = % = △ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 △ 3 ⊕ 8 ◇ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-46022",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 △ 3 ⊕ 8 ◇ 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 = 4 * y ** y + x;
otherwise, x ☆ y = x - x + y - 1.
and □, the rules are as follows:
when y is even, x □ y = x + y;
otherwise, x □ y = x + y.
The precedence of operations: ☆ > ** > * = / = % > + = - = □。
Parentheses have the highest prior... | {
"game_data": {
"answer": "25",
"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:
when x and y are both odd, x ◇ y = (x ** y / x) * y ** 1;
otherwise, x ◇ y = abs(2 * x * 5) * y + 3.
The precedence of operations: ** > * = / = % > + = - = ◇。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate th... | {
"game_data": {
"answer": "27",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ◇ 3 % 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 x is even, x □ y = y - y + x * y + 4;
otherwise, x □ y = x * (y + 2).
and ⊙, the rules are as follows:
when y is odd, x ⊙ y = x + x - y □ x / x;
otherwise, x ⊙ y = y * y + x / x * y.
The precedence of operations: ** > * = / = % > + = - = □ = ⊙。
Parentheses have the highe... | {
"game_data": {
"answer": "56",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 □ 4 ⊙ 3 ⊙ 7",
"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 = 4 + x + y。
和 ⊙，规则如下：
实数域上，x ⊙ y = x + y - 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: 7 ⊙ 7 ◎ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "23",
"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 | 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: 8 △ 4
Please fill your fin... | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 △ 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 is a multiple of 5, x ◎ y = x * 5 ** y - 3;
otherwise, x ◎ y = y * x * y + x.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = x * y.
The precedence of operations: ** = ⊗ > * = / = % = ◎ > + = -。
Parentheses have the highest priority, and the expression... | {
"game_data": {
"answer": "78",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ◎ 1 ⊗ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dep... |
logic-v2 | Define ◎, the rules are as follows:
when x is a multiple of 5, x ◎ y = y - x * y - x - y;
otherwise, x ◎ y = x + x * x * 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... | {
"game_data": {
"answer": "39",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 △ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth":... |
logic-v2 | 定义 ☆，规则如下：
实数域上，x ☆ y = 5 - 1 + x - y * 5。
和 ⊗，规则如下：
实数域上，x ⊗ y = x - x ☆ y * y。
运算优先级：** > * = / = % = ☆ > + = - = ⊗。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 ☆ 7 ⊗ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "343",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ☆ 7 ⊗ 7",
"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和y都是偶数时，x ⊗ y = x + x - y + x；
其他情况下，x ⊗ y = y + x - y。
和 ☆，规则如下：
实数域上，x ☆ y = 3 - y - x。
和 ♡，规则如下：
实数域上，x ♡ y = y * 5 ⊗ x。
运算优先级：** = ♡ > * = / = % = ☆ > + = - = ⊗。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 ♡ 1 ⊗ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ♡ 1 ⊗ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dept... |
logic-v2 | 定义 □，规则如下：
实数域上，x □ y = y - abs(x * 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 = abs(2 * x) * y。
运算优先级：⊙ > ** = □ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 ⊙ 5 □ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-9995",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ⊙ 5 □ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting... |
logic-v2 | 定义 ☆，规则如下：
当x大于y时，x ☆ y = x + y * y * (y)；
其他情况下，x ☆ y = 3 - x - y - x。
和 △，规则如下：
实数域上，x △ y = (y + x) + x / x。
运算优先级：☆ > ** = △ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 ☆ 6 ☆ 10 △ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1237",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ☆ 6 ☆ 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 * 5 - x + y.
and ◇, the rules are as follows:
when x and y are both even, x ◇ y = x + y;
otherwise, x ◇ y = y ⊗ (x) ** 1 + y.
and ☆, the rules are as follows:
on the real number field, x ☆ y = x ◇ y + y + y.
The precedence of operations: **... | {
"game_data": {
"answer": "81",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ◇ 3 ⊗ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dep... |
logic-v2 | 定义 △，规则如下：
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: 2 △ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "18",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 △ 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:
on the real number field, x ⊗ y = x - y / x * 1 - 2.
and ▽, the rules are as follows:
when x is a multiple of 3, x ▽ y = (y + x);
otherwise, x ▽ y = x + x * x - y.
and ☆, the rules are as follows:
on the real number field, x ☆ y = y + 3 - 4 + x.
The precedence of operations: ... | {
"game_data": {
"answer": "-4.888889",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ⊗ 1 ▽ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nest... |
logic-v2 | Define □, the rules are as follows:
when x is a multiple of 5, x □ y = 1 + x / y;
otherwise, x □ y = x / y * x + y.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = 5 □ x * x - y.
The precedence of operations: ⊗ > ** = □ > * = / = % > + = -。
Parentheses have the highest priority, and the express... | {
"game_data": {
"answer": "10.777778",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 □ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_... |
logic-v2 | 定义 ⊕，规则如下：
实数域上，x ⊕ y = x - y / x。
和 ▽，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 - 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 ♡ 6 ▽ 5 ⊕ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ♡ 4 ♡ 6 ▽ 5 ⊕ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nes... |
logic-v2 | 定义 ▽，规则如下：
当x和y都是偶数时，x ▽ y = x - y - x；
其他情况下，x ▽ 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: 1 ** 5 ▽ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ** 5 ▽ 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 = y - 3 + x.
and ☆, the rules are as follows:
on the real number field, x ☆ y = 2 + x * (y).
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = x + x ☆ y.
The precedence of operations: ☆ > ** = ⊕ > * = / = % > + = - = ⊙。
Parenthes... | {
"game_data": {
"answer": "23",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ⊕ 8 ☆ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dep... |
logic-v2 | 定义 ⊗，规则如下：
当x是3的倍数时，x ⊗ y = 1 * (x ** y) - x；
其他情况下，x ⊗ y = y - y / abs(y * x / x)。
和 ◇，规则如下：
实数域上，x ◇ y = y - y * x + abs(4 - y)。
和 ⊕，规则如下：
实数域上，x ⊕ 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 ◇ 10 ⊗ 8 ⊕ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-107",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ◇ 10 ⊗ 8 ⊕ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nest... |
logic-v2 | Define □, the rules are as follows:
when y is a multiple of 3, x □ y = y * x - 3;
otherwise, x □ y = x * y.
and ◇, the rules are as follows:
on the real number field, x ◇ y = x - 3 □ y.
The precedence of operations: □ > ** > * = / = % > + = - = ◇。
Parentheses have the highest priority, and the expression inside t... | {
"game_data": {
"answer": "-39",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ◇ 3 □ 5 + 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nestin... |
logic-v2 | Define ◇, the rules are as follows:
on the real number field, x ◇ y = x + y.
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 ◇ 9
Please fill your final answer... | {
"game_data": {
"answer": "12",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ◇ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"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 + y)。
和 ◇，规则如下：
当x小于y时，x ◇ y = x + 2 + y；
其他情况下，x ◇ y = y ⊙ y - x。
运算优先级：⊙ > ** > * = / = % > + = - = △ = ◇。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7 ◇ 7 ⊙ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "37",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ◇ 7 ⊙ 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:
on the real number field, x ○ y = x * y.
The precedence of operations: ** > * = / = % > + = - = ○。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 8
Please fill your final answer in ... | {
"game_data": {
"answer": "8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null... |
logic-v2 | Define ⊗, the rules are as follows:
on the real number field, x ⊗ y = x * 1 + y + y.
and ◎, the rules are as follows:
when x is greater than y, x ◎ y = x + y ⊗ 1;
otherwise, x ◎ y = y * 5 ** y - x.
and ▽, the rules are as follows:
when x is less than y, x ▽ y = y ** y ◎ x - y;
otherwise, x ▽ y = y + y + y + x... | {
"game_data": {
"answer": "2443",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ⊗ 9 ▽ 5 / 1 ◎ 4",
"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 less than y, x △ y = x - x - y;
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: 4 ... | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 % 8 △ 10 % 5",
"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 - y - x.
The precedence of operations: ** = ◇ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 9 + 6 ◇ 3 ** 5
Please fill your... | {
"game_data": {
"answer": "-234",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 + 6 ◇ 3 ** 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nest... |
logic-v2 | Define □, the rules are as follows:
when y is even, x □ y = y - x * (2) - x;
otherwise, x □ y = y - y + y / x.
and △, 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 i... | {
"game_data": {
"answer": "3.285714",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 △ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_d... |
logic-v2 | 定义 ♢，规则如下：
当y是奇数时，x ♢ y = x + y * x * y；
其他情况下，x ♢ y = y - (x / x - x) - x。
和 ○，规则如下：
实数域上，x ○ y = y - x - 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: 8 ♢ 2 - 6 / 2 ○ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ♢ 2 - 6 / 2 ○ 9",
"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 + x.
and ♢, the rules are as follows:
on the real number field, x ♢ y = (3) - y □ x - y.
The precedence of operations: ** = ♢ > * = / = % > + = - = □。
Parentheses have the highest priority, and the expression inside the parentheses is calculate... | {
"game_data": {
"answer": "7",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 □ 4 ♢ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dep... |
logic-v2 | 定义 ◎，规则如下：
实数域上，x ◎ y = (y - y - x) * 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: 2 △ 9 ◎ 6 - 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "156",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 △ 9 ◎ 6 - 8",
"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 = abs(y) + x - x。
和 ♢，规则如下：
当x和y都是偶数时，x ♢ y = y * abs(2) / x；
其他情况下，x ♢ y = x / y * 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: 2 * 3 □ 6 ♢ 6 / 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0.4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 * 3 □ 6 ♢ 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大于y时，x △ y = y * x * y * x - y；
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: 7 △ 9 △ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "3.4375",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 △ 9 △ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting... |
logic-v2 | Define ○, the rules are as follows:
on the real number field, x ○ y = y / x * y.
The precedence of operations: ** > * = / = % = ○ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 5 ○ 6
Please fill your final an... | {
"game_data": {
"answer": "7.2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ○ 6",
"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 - y；
其他情况下，x ☆ y = abs(x * y)。
和 △，规则如下：
实数域上，x △ y = y ☆ x - y。
运算优先级：☆ > △ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 △ 10 ☆ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "60",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 △ 10 ☆ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_de... |
logic-v2 | Define ☆, the rules are as follows:
when x is even, x ☆ y = 2 + y + abs(y) * x;
otherwise, x ☆ y = y + x - 3.
and △, the rules are as follows:
on the real number field, x △ y = 1 + y * x.
The precedence of operations: ** > * = / = % = ☆ = △ > + = -。
Parentheses have the highest priority, and the expression inside... | {
"game_data": {
"answer": "86",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ☆ 2 ☆ 3 △ 5",
"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 + y * 3 * (x - 1).
and ♢, the rules are as follows:
on the real number field, x ♢ y = x / y - (y).
and ○, the rules are as follows:
on the real number field, x ○ y = y + x - (x) * 5 ⊙ y.
The precedence of operations: ** = ⊙ = ♢ > * = / = % > ... | {
"game_data": {
"answer": "-67.0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ⊙ 7 ♢ 6 ○ 1",
"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 = 5 + y + 4 - x * y。
和 ○，规则如下：
实数域上，x ○ y = 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: 2 ○ 3 ⊙ 1 % 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1.5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ○ 3 ⊙ 1 % 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nestin... |
logic-v2 | Define △, the rules are as follows:
when y is odd, x △ y = y * x + x;
otherwise, x △ y = y + x + 3 - 2.
The precedence of operations: △ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 4 △ 2 ... | {
"game_data": {
"answer": "2401",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 △ 2 ** 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_... |
logic-v2 | 定义 □，规则如下：
当x大于y时，x □ y = x + y + x；
其他情况下，x □ y = x * y + x + x。
和 ○，规则如下：
实数域上，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: 9 / 8 □ 1 ○ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0.102273",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 / 8 □ 1 ○ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"n... |
logic-v2 | 定义 ☆，规则如下：
当y是偶数时，x ☆ y = 3 / y - 2 - x * x；
其他情况下，x ☆ y = x * (2 * x + 1) * y。
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 = 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 % 2 ☆ 9 ◎ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 % 2 ☆ 9 ◎ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting... |
logic-v2 | Define △, the rules are as follows:
when y is odd, x △ y = x - x + x - y ** x;
otherwise, x △ y = 5 + y * 5 - x + 3.
The precedence of operations: △ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expre... | {
"game_data": {
"answer": "44",
"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 | 定义 ⊗，规则如下：
当y是偶数时，x ⊗ y = abs(x * x * y)；
其他情况下，x ⊗ y = (y) + x * y - y。
和 ◇，规则如下：
实数域上，x ◇ y = y + x * y - x。
和 ⊕，规则如下：
当x和y都是奇数时，x ⊕ y = y / y * y / x；
其他情况下，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: 8 ⊗ 2 ⊕ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "10.000781",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ⊗ 2 ⊕ 10",
"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 + x * y.
The precedence of operations: ** = ◇ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 2 - 5 - 7 ◇ 8
Please fill your ... | {
"game_data": {
"answer": "-66",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 - 5 - 7 ◇ 8",
"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 = (x) / y + x;
otherwise, x ⊙ y = 3 * y + x * x.
and ▽, the rules are as follows:
when x is even, x ▽ y = abs(x - x + y * y);
otherwise, x ▽ y = x - y - x.
The precedence of operations: ** = ⊙ > * = / = % > + = - = ▽。
Parentheses have the high... | {
"game_data": {
"answer": "108",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ⊙ 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 = x + y。
运算优先级：** > * = / = % > + = - = ▽。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | 定义 ♢，规则如下：
实数域上，x ♢ y = 1 - y - x * 4 + y。
和 ▽，规则如下：
实数域上，x ▽ y = y - (x ** y + x - 1)。
和 ◎，规则如下：
实数域上，x ◎ y = 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 ◎ 9 ▽ 2 % 3 ♢ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-10",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ◎ 9 ▽ 2 % 3 ♢ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"ne... |
logic-v2 | 定义 ▽，规则如下：
实数域上，x ▽ y = x * x / y。
运算优先级：▽ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 ▽ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "12.5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ▽ 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:
when y is odd, x ◇ y = y - y / x;
otherwise, x ◇ y = y * x * 2 * 4.
The precedence of operations: ** > * = / = % > + = - = ◇。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 8 ◇ 5 ... | {
"game_data": {
"answer": "175",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ◇ 5 * 1 ◇ 5",
"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 + y - x * y。
和 ☆，规则如下：
实数域上，x ☆ y = y □ y / x - x / y。
运算优先级：□ > ** > * = / = % > + = - = ☆。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5 ☆ 4 ☆ 2 □ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "19.768445",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ☆ 4 ☆ 2 □ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"... |
logic-v2 | Define △, the rules are as follows:
when y is odd, x △ y = abs(x) + y + 1;
otherwise, x △ y = x * x - y + y.
The precedence of operations: △ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 2... | {
"game_data": {
"answer": "18",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 % 7 △ 8 * 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting... |
logic-v2 | 定义 □，规则如下：
当x和y都是偶数时，x □ y = y + y + x；
其他情况下，x □ y = 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 □ 10 ⊕ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 □ 10 ⊕ 6",
"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 = x + y - y + x + y.
and △, the rules are as follows:
on the real number field, x △ y = y * y - x ⊗ x + 5.
and ♡, the rules are as follows:
on the real number field, x ♡ y = y - x + x + x.
The precedence of operations: ♡ > ⊗ > ** = △ > * = / = % ... | {
"game_data": {
"answer": "-3273",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 △ 5 ⊗ 6 ⊗ 2 △ 7 ♡ 6",
"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 = x + y - x.
and ⊗, the rules are as follows:
when x and y are both odd, x ⊗ y = y ** (x) * y;
otherwise, x ⊗ y = y * y - x.
The precedence of operations: ⊗ > ⊕ > ** ... | {
"game_data": {
"answer": "-12",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ⊗ 2 ⊙ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_de... |
logic-v2 | 定义 ♡，规则如下：
当x是偶数时，x ♡ y = x ** y + y - y；
其他情况下，x ♡ y = y - x ** x。
和 ⊗，规则如下：
当x和y的和是偶数时，x ⊗ y = x ** (y + x)；
其他情况下，x ⊗ y = x * y + 5。
运算优先级：♡ > ** > * = / = % > + = - = ⊗。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 ♡ 2 + 9 ⊗ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "105",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ♡ 2 + 9 ⊗ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nestin... |
logic-v2 | 定义 △，规则如下：
实数域上，x △ y = 5 + 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
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | 定义 ♡，规则如下：
实数域上，x ♡ y = x + x - y。
和 ◎，规则如下：
当y是奇数时，x ◎ y = x - y ♡ y；
其他情况下，x ◎ y = (x) - y + x。
运算优先级：◎ > ♡ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 ◎ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "10",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ◎ 10",
"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。
和 ☆，规则如下：
当y是3的倍数时，x ☆ y = y * y ⊕ x；
其他情况下，x ☆ y = y - x / x。
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 * 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 ☆ 1 ○ 3 ⊕ 4 ⊕ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-20",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ☆ 1 ○ 3 ⊕ 4 ⊕ 7",
"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大于y时，x △ y = 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: 2 + 9 * 3 △ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-25",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 + 9 * 3 △ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesti... |
logic-v2 | 定义 ◇，规则如下：
实数域上，x ◇ y = 3 - y * x - x。
和 ☆，规则如下：
当x大于y时，x ☆ y = y * y * x；
其他情况下，x ☆ y = y + abs(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: 1 ◇ 7 ☆ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-18",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ◇ 7 ☆ 7",
"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 x and y are both even, x ☆ y = x * y * 4 - y;
otherwise, x ☆ y = y * y + y + x.
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = x - y * (y) ☆ y.
The precedence of operations: ** = ⊙ > * = / = % = ☆ > + = -。
Parentheses have the highest priority, and the ... | {
"game_data": {
"answer": "-178",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ⊙ 2 ☆ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_d... |
logic-v2 | 定义 ◇，规则如下：
当x和y的和是偶数时，x ◇ y = x * x + x - y；
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: 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等于y时，x ⊕ y = y - x + x ** x；
其他情况下，x ⊕ y = x * y + y + y。
和 ♢，规则如下：
实数域上，x ♢ y = 1 ⊕ y * (y) - x。
和 ⊗，规则如下：
当x大于y时，x ⊗ y = y * x - x；
其他情况下，x ⊗ y = y / 2 + x。
运算优先级：⊕ > ⊗ > ** > * = / = % > + = - = ♢。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 ⊗ 5 ⊕ 9 ♢ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "74.5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ⊗ 5 ⊕ 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:
on the real number field, x ▽ y = 2 / x / y / 2.
The precedence of operations: ** > * = / = % > + = - = ▽。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 9 ▽ 10 + 10
Please fill you... | {
"game_data": {
"answer": "10.011111",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ▽ 10 + 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"ne... |
logic-v2 | Define ○, the rules are as follows:
on the real number field, x ○ y = x + y - y.
The precedence of operations: ** = ○ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 8
Please fill your final answer... | {
"game_data": {
"answer": "8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null... |
logic-v2 | 定义 ◇，规则如下：
当x等于y时，x ◇ y = x + x + y；
其他情况下，x ◇ y = x + x * y * x。
运算优先级：◇ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 - 3 ◇ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-91",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 - 3 ◇ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_d... |
logic-v2 | Define ♢, the rules are as follows:
when x is a multiple of 5, x ♢ y = y - x - x;
otherwise, x ♢ y = 5 + (x) * y / 1.
and ⊕, the rules are as follows:
when x is a multiple of 5, x ⊕ y = x * y - y ♢ y;
otherwise, x ⊕ y = x ♢ x - (x * y).
and □, the rules are as follows:
on the real number field, x □ y = y + x ... | {
"game_data": {
"answer": "89",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ⊕ 7 □ 9 ♢ 3",
"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 * y - y / 1.
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 parentheses is calcula... | {
"game_data": {
"answer": "-48",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ◇ 9 ◎ 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 = 4 + x - x * y;
otherwise, x ⊙ y = x + x - y.
and △, the rules are as follows:
when y is a multiple of 5, x △ y = x + y - 2;
otherwise, x △ y = x + y / y * y.
and ○, the rules are as follows:
on the real number field, x ○ y = x * x - y - y... | {
"game_data": {
"answer": "56",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ○ 3 ⊙ 1 △ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting... |
logic-v2 | 定义 ◇，规则如下：
当x是偶数时，x ◇ y = 2 + y + x - y ** 2；
其他情况下，x ◇ y = x + 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 % 7 ◇ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 % 7 ◇ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dept... |
logic-v2 | Define ⊕, the rules are as follows:
when x is odd, x ⊕ y = x - abs(4 * y) - x;
otherwise, x ⊕ y = x / x + y * x.
and ♢, 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 odd, x ◎ y = 4 + x ** y * x;
otherwise, x ◎ y = 4 * x + 3 ⊕ y.
The prec... | {
"game_data": {
"answer": "-32",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ⊕ 5 ♢ 10 ◎ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesti... |
logic-v2 | 定义 ♢，规则如下：
当x是3的倍数时，x ♢ y = x + (x + y)；
其他情况下，x ♢ y = x + y - y / x * y。
和 □，规则如下：
实数域上，x □ y = x ♢ x - (y) + y。
和 ◎，规则如下：
当y是5的倍数时，x ◎ y = 2 - x - y + x - 2；
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 ♢ 1 ◎ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "4.428571",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ♢ 1 ◎ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesti... |
logic-v2 | Define ◎, the rules are as follows:
on the real number field, x ◎ y = y + x - y.
and ⊙, the rules are as follows:
when the sum of x and y is even, x ⊙ y = 2 * x + y;
otherwise, x ⊙ y = y * x.
The precedence of operations: ◎ > ** > * = / = % = ⊙ > + = -。
Parentheses have the highest priority, and the expression in... | {
"game_data": {
"answer": "72",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ⊙ 3 ** 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 = y / x - 5 * y * x.
and ▽, the rules are as follows:
when x and y are both even, x ▽ y = y ** y + x - x ** y;
otherwise, x ▽ y = x - y - abs(x) - x.
The precedence of operations: ☆ > ** > * = / = % > + = - = ▽。
Parentheses have the highest prior... | {
"game_data": {
"answer": "98.8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 - 9 ▽ 10 ☆ 2",
"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 = (1 / x + 3 - x) * y。
和 ⊙，规则如下：
当y是偶数时，x ⊙ y = y ⊗ x / x - x；
其他情况下，x ⊙ y = (5 ⊗ y + x) - x。
和 ○，规则如下：
实数域上，x ○ y = 2 ⊗ x + y - 4 / 3。
运算优先级：⊙ > ** > * = / = % = ○ > + = - = ⊗。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 ⊙ 3 ⊗ 1 ○ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "34.228395",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ⊙ 3 ⊗ 1 ○ 4",
"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 + y + x + y.
and △, the rules are as follows:
on the real number field, x △ y = 1 ⊙ y / y * x - 2.
and ⊕, the rules are as follows:
on the real number field, x ⊕ y = y + y / x.
The precedence of operations: ** > * = / = % = ⊙ > + = - = △ = ⊕。... | {
"game_data": {
"answer": "16.666667",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ⊕ 1 ⊙ 1 △ 1",
"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 = y * x;
otherwise, x ⊗ y = x + y + y.
and ⊕, the rules are as follows:
when x is greater than y, x ⊕ y = x ⊗ y - y;
otherwise, x ⊕ y = y * x ⊗ x.
and ☆, the rules are as follows:
on the real number field, x ☆ y = (x ⊕ y) + x.
The precedence of ... | {
"game_data": {
"answer": "128",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ☆ 10 ⊕ 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 = x - 1 / y。
和 ◎，规则如下：
当x大于y时，x ◎ y = x - y - y + 1；
其他情况下，x ◎ y = y □ x + 5。
运算优先级：□ = ◎ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 ◎ 7 □ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "11.5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ◎ 7 □ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_d... |
logic-v2 | Define ○, the rules are as follows:
when x is odd, x ○ y = x + y - 3 + 3;
otherwise, x ○ y = y - x + y + y.
The precedence of operations: ** = ○ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 1 ... | {
"game_data": {
"answer": "9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ○ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": ... |
logic-v2 | 定义 ◇，规则如下：
当x和y都是偶数时，x ◇ y = (x * y / 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: 10 ◇ 1 - 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-5.888889",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ◇ 1 - 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nes... |
logic-v2 | Define ◇, the rules are as follows:
when y is a multiple of 5, x ◇ y = y - x - y;
otherwise, x ◇ y = x + y + y.
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": "16.571429",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ◇ 8 - 3 / 7",
"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 greater than y, x ○ y = x * 5 + y;
otherwise, x ○ y = y ** x * x.
The precedence of operations: ○ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression... | {
"game_data": {
"answer": "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 = 3 + (y * x * x)。
运算优先级：▽ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 / 4 ▽ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0.072289",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 / 4 ▽ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesti... |
logic-v2 | Define ○, the rules are as follows:
when y is odd, x ○ y = x + x + y + abs(y);
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": "18",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ○ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth":... |
logic-v2 | Define ⊙, the rules are as follows:
when x is greater than y, x ⊙ y = y - y - x;
otherwise, x ⊙ y = y * x + y - x.
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 = y ◇ x - x - y.
The precedence of operations: ◇ > ** ... | {
"game_data": {
"answer": "-8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ⊙ 1 ◇ 3 ▽ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nestin... |
logic-v2 | Define ♡, the rules are as follows:
when x and y are both odd, x ♡ y = (x * y);
otherwise, x ♡ y = 5 * 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 insi... | {
"game_data": {
"answer": "77",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ⊙ 3 ♡ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_de... |
logic-v2 | 定义 ♢，规则如下：
当y是3的倍数时，x ♢ y = y ** 5 * x；
其他情况下，x ♢ y = 5 + 1 - x + y / y。
和 △，规则如下：
实数域上，x △ y = y * x - y * 1。
和 ♡，规则如下：
当x和y的和是奇数时，x ♡ y = y - y + x + x；
其他情况下，x ♡ y = y * y * x + y / y。
运算优先级：♢ > △ > ** > * = / = % > + = - = ♡。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 ♡ 4 △ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "12",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ♡ 4 △ 1",
"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：
当x和y的和是奇数时，x ☆ y = y / x；
其他情况下，x ☆ y = x - y ♡ y。
运算优先级：♡ > ☆ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 9 ** 7 ☆ 7 ♡ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "81",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ** 7 ☆ 7 ♡ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nestin... |
logic-v2 | Define ▽, the rules are as follows:
on the real number field, x ▽ y = x * x + x - y.
The precedence of operations: ▽ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 9 % 1 ▽ 5
Please fill your ... | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 % 1 ▽ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dept... |
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