env stringclasses 1
value | prompt stringlengths 119 673 | extra dict |
|---|---|---|
logic-v2 | 定义 ◇，规则如下：
实数域上，x ◇ y = x + y + y。
运算优先级：** > * = / = % > + = - = ◇。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ◇ 3 - 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ◇ 3 - 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dept... |
logic-v2 | 定义 ○，规则如下：
当x和y都是偶数时，x ○ y = (y + x + x) + 1；
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: 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",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": nu... |
logic-v2 | Define ☆, the rules are as follows:
on the real number field, x ☆ y = y * 3 * x - 2.
and ○, the rules are as follows:
on the real number field, x ○ y = x + y.
The precedence of operations: ** = ○ > * = / = % > + = - = ☆。
Parentheses have the highest priority, and the expression inside the parentheses is calculated ... | {
"game_data": {
"answer": "-2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 % 3 ☆ 4 ○ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting... |
logic-v2 | 定义 ⊕，规则如下：
实数域上，x ⊕ y = y ** 2 * 2 * x - y。
和 ♡，规则如下：
实数域上，x ♡ y = y + abs(2) + x。
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: 9 ○ 10 ⊕ 6 ♡ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "700",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ○ 10 ⊕ 6 ♡ 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 y is even, x △ y = y + x;
otherwise, x △ y = (x) * y.
The precedence of operations: ** > * = / = % = △ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 4 △ 9
Please fi... | {
"game_data": {
"answer": "36",
"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_depth":... |
logic-v2 | 定义 ○，规则如下：
当x等于y时，x ○ y = x * abs(y) - y；
其他情况下，x ○ y = 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: 1 + 1 ○ 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 + 1 ○ 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:
on the real number field, x ◇ y = x + y - 3 + y.
The precedence of operations: ** > * = / = % > + = - = ◇。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 1
Please fill your final an... | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null... |
logic-v2 | Define ⊗, the rules are as follows:
on the real number field, x ⊗ y = 3 * 1 * 5 + x + y.
and □, the rules are as follows:
when x is odd, x □ y = x + y ⊗ y - 4 + y;
otherwise, x □ y = y ⊗ x + 4.
and ♢, the rules are as follows:
when x and y are both odd, x ♢ y = x - y □ y * x;
otherwise, x ♢ y = x ⊗ y * y - y.... | {
"game_data": {
"answer": "303",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ♢ 7 □ 2 ⊗ 8",
"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 * 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: 5 ** 4 ○ 9
Please fill your fin... | {
"game_data": {
"answer": "50625",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ** 4 ○ 9",
"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 + 5 + y.
and △, the rules are as follows:
on the real number field, x △ y = 2 + y ⊙ x + y.
and ☆, the rules are as follows:
when the sum of x and y is even, x ☆ y = x / y + y / x;
otherwise, x ☆ y = x - x * y △ x.
The precedence of oper... | {
"game_data": {
"answer": "14",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ⊙ 10 △ 10 ☆ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesti... |
logic-v2 | 定义 ⊙，规则如下：
当y是奇数时，x ⊙ y = x ** y；
其他情况下，x ⊙ y = y - x * x - y。
和 ☆，规则如下：
当y是5的倍数时，x ☆ y = y * x ⊙ 1 + y；
其他情况下，x ☆ 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: 9 ○ 6 ☆ 8 ⊙ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-324",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ○ 6 ☆ 8 ⊙ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesti... |
logic-v2 | Define ▽, the rules are as follows:
when x is less than y, x ▽ y = x * y + y;
otherwise, x ▽ y = x * y * y.
The precedence of operations: ** = ▽ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 7
... | {
"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：
当x和y都是偶数时，x ♢ y = y + abs(y + x)；
其他情况下，x ♢ y = x + y * y * y / y。
和 ◎，规则如下：
实数域上，x ◎ y = x ♢ x ** x - x + y。
和 ⊙，规则如下：
实数域上，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: 2 ♢ 8 ⊙ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "194",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ♢ 8 ⊙ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_de... |
logic-v2 | Define ♡, the rules are as follows:
when x is even, x ♡ y = y * x;
otherwise, x ♡ y = x / 4 - x - y.
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = y * x.
The precedence of operations: ♡ = ⊙ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parenthe... | {
"game_data": {
"answer": "-18.75",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ♡ 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:
when y is even, x ○ y = (x + x) - y;
otherwise, x ○ y = x * y.
The precedence of operations: ** > * = / = % = ○ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 9
Please fi... | {
"game_data": {
"answer": "9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null... |
logic-v2 | Define ⊗, the rules are as follows:
on the real number field, x ⊗ y = y / abs(x + 2 * 5).
and △, the rules are as follows:
on the real number field, x △ y = 4 - y - x ⊗ x.
and ○, the rules are as follows:
on the real number field, x ○ y = y + y - y + x.
The precedence of operations: ⊗ > ** > * = / = % = △ > + = -... | {
"game_data": {
"answer": "6.625",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 △ 1 ○ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_... |
logic-v2 | Define ▽, the rules are as follows:
on the real number field, x ▽ y = x * (x - y * y).
The precedence of operations: ▽ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 9 * 5 ▽ 4 % 10
Please fil... | {
"game_data": {
"answer": "5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 * 5 ▽ 4 % 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting... |
logic-v2 | 定义 ◎，规则如下：
实数域上，x ◎ y = (y ** x) + 1。
和 △，规则如下：
当x是5的倍数时，x △ y = (y ◎ x) - y；
其他情况下，x △ y = x + x * y。
运算优先级：◎ > ** = △ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 ◎ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ◎ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": ... |
logic-v2 | 定义 ◇，规则如下：
当x是3的倍数时，x ◇ y = x * y - x + 5 - 3；
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: 1 + 9 ◇ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "21",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 + 9 ◇ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dep... |
logic-v2 | Define ◇, the rules are as follows:
when x is even, x ◇ y = 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: 4 ◇ 7
Please ... | {
"game_data": {
"answer": "11",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ◇ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth":... |
logic-v2 | 定义 ⊕，规则如下：
实数域上，x ⊕ y = (y + y) + x。
和 ◇，规则如下：
实数域上，x ◇ y = (x) - x ⊕ y。
和 △，规则如下：
当y是5的倍数时，x △ y = y ◇ x - y - (x)；
其他情况下，x △ y = (y * x)。
运算优先级：** = ⊕ > * = / = % = ◇ > + = - = △。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 △ 2 △ 2 ◇ 10 / 1 ⊕ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-21.333333",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 △ 2 △ 2 ◇ 10 / 1 ⊕ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": nul... |
logic-v2 | 定义 ☆，规则如下：
当x小于y时，x ☆ y = y + y * x；
其他情况下，x ☆ y = x + x - y。
和 ♢，规则如下：
实数域上，x ♢ y = x ☆ y * x。
运算优先级：♢ > ☆ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 ♢ 1 ☆ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "125",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ♢ 1 ☆ 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 is equal to y, x ▽ y = 1 - x / y;
otherwise, x ▽ y = x * y.
The precedence of operations: ▽ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 6 % 5 ▽... | {
"game_data": {
"answer": "6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 % 5 ▽ 1 ** 10",
"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和y的和是奇数时，x □ y = x + y；
其他情况下，x □ y = x * y ** y。
和 ♡，规则如下：
当y是3的倍数时，x ♡ y = y + abs(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: 9 ♡ 10 + 4 □ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ♡ 10 + 4 □ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nestin... |
logic-v2 | Define ♢, the rules are as follows:
when x and y are both even, x ♢ y = abs(y + x) / x;
otherwise, x ♢ y = y / x * x.
and ♡, the rules are as follows:
on the real number field, x ♡ y = x ♢ x * y.
and ⊙, the rules are as follows:
when x is a multiple of 3, x ⊙ y = y + x;
otherwise, x ⊙ y = y - (x) - x.
The pre... | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ♢ 9 ⊙ 6 ♡ 10 - 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nes... |
logic-v2 | Define ♢, the rules are as follows:
when y is odd, x ♢ y = y * x - y - y;
otherwise, x ♢ y = (5 * x) / y.
and ♡, the rules are as follows:
on the real number field, x ♡ y = 2 / y - x.
and ☆, the rules are as follows:
on the real number field, x ☆ y = y + x.
The precedence of operations: ♢ > ** > * = / = % = ♡ >... | {
"game_data": {
"answer": "-8.3",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ♡ 10 ☆ 3 ♢ 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 + 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: 1
Please fill your fina... | {
"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 | 定义 ○，规则如下：
当y是5的倍数时，x ○ y = x - y / x；
其他情况下，x ○ y = y + x。
运算优先级：** = ○ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 * 3 ○ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "90",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 * 3 ○ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_de... |
logic-v2 | 定义 ▽，规则如下：
实数域上，x ▽ y = y - y + (x)。
运算优先级：** = ▽ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 ▽ 3 % 5 - 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ▽ 3 % 5 - 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nestin... |
logic-v2 | Define ♡, the rules are as follows:
when x is equal to y, x ♡ y = x * y - y + y;
otherwise, x ♡ y = x * 1 - 3 - y * y.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = x * (x / y) + y - y.
The precedence of operations: ♡ > ** > * = / = % > + = - = ⊗。
Parentheses have the highest priority, and th... | {
"game_data": {
"answer": "-0.818182",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ⊗ 7 ♡ 8 ♡ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"... |
logic-v2 | Define ☆, the rules are as follows:
when x and y are both even, x ☆ y = x / y ** y * y;
otherwise, x ☆ y = y - x * x.
and ♢, the rules are as follows:
when y is odd, x ♢ y = y - (x / x ☆ y) * y;
otherwise, x ♢ y = (y + x ☆ y).
The precedence of operations: ** = ☆ > * = / = % > + = - = ♢。
Parentheses have the hi... | {
"game_data": {
"answer": "4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ☆ 2 ♢ 10",
"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是偶数时，x ◇ y = y + x - y；
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: 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | 定义 ♢，规则如下：
实数域上，x ♢ y = 2 * x * abs(y)。
和 △，规则如下：
实数域上，x △ y = y + abs(x - x)。
和 ⊕，规则如下：
当y是偶数时，x ⊕ y = 3 + x ♢ y；
其他情况下，x ⊕ y = x + y + x。
运算优先级：△ = ⊕ > ** > * = / = % = ♢ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 △ 10 ⊕ 8 ♢ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1304",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 △ 10 ⊕ 8 ♢ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nest... |
logic-v2 | 定义 ◇，规则如下：
当y是偶数时，x ◇ y = x + 2 + y + y；
其他情况下，x ◇ y = y - x + y。
运算优先级：** > * = / = % > + = - = ◇。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 / 6 / 4 ◇ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "19.875",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 / 6 / 4 ◇ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"ne... |
logic-v2 | Define ⊕, the rules are as follows:
when y is a multiple of 3, x ⊕ y = x * y - y;
otherwise, x ⊕ y = y - x + x.
and ⊙, the rules are as follows:
when x is even, x ⊙ y = x - y + y;
otherwise, x ⊙ y = 1 - x * y.
and ♡, the rules are as follows:
when x and y are both odd, x ♡ y = y + x + y;
otherwise, x ♡ y = ... | {
"game_data": {
"answer": "0.62963",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ⊕ 5 / 6 ♡ 10 % 6 ⊙ 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 = 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: 6 ▽ 8
Please fill your final an... | {
"game_data": {
"answer": "6.75",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ▽ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth... |
logic-v2 | Define ▽, the rules are as follows:
on the real number field, x ▽ y = y + x * x.
and △, the rules are as follows:
when y is odd, x △ y = x * y - x;
otherwise, x △ y = x + 5 + y.
The precedence of operations: ** = ▽ = △ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the paren... | {
"game_data": {
"answer": "3640",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 * 8 △ 6 ▽ 3",
"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 = abs(x - y) + y * x。
和 △，规则如下：
当x是偶数时，x △ y = y + y ◎ 4 - 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: 9 △ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-18",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 △ 3",
"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 + 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: 9 + 8 ♡ 1 ◎ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "12.375",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 + 8 ♡ 1 ◎ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nes... |
logic-v2 | 定义 ♡，规则如下：
当y是5的倍数时，x ♡ y = 1 - y + 4 / x；
其他情况下，x ♡ y = x + 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: 1 ♡ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "7",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ♡ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": ... |
logic-v2 | Define ○, the rules are as follows:
on the real number field, x ○ y = x - y + y + abs(x).
The precedence of operations: ** = ○ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 8 ○ 9
Please fill your... | {
"game_data": {
"answer": "16",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ○ 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 = 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: 3 ○ 8
Please fill your fina... | {
"game_data": {
"answer": "24",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ○ 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是奇数时，x ○ y = x - y - x；
其他情况下，x ○ y = abs(y ** x + x)。
运算优先级：** > * = / = % > + = - = ○。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | Define △, the rules are as follows:
on the real number field, x △ y = abs(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 △ 7
Please fill your fin... | {
"game_data": {
"answer": "7",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 △ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": ... |
logic-v2 | Define ▽, the rules are as follows:
on the real number field, x ▽ y = 3 ** 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 ▽ 1 * 10
Please fill your fi... | {
"game_data": {
"answer": "810",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ▽ 1 * 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_d... |
logic-v2 | Define □, the rules are as follows:
when x is even, x □ y = x + y - 5 + y + y;
otherwise, x □ y = x - x * y - 2 - x.
and ◇, the rules are as follows:
on the real number field, x ◇ y = 3 - y - x * x.
The precedence of operations: ◇ > ** > * = / = % = □ > + = -。
Parentheses have the highest priority, and the expres... | {
"game_data": {
"answer": "-166",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 □ 7 ◇ 9",
"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 * 3 - x.
and □, the rules are as follows:
when y is a multiple of 3, x □ y = 4 ** (y) ☆ x;
otherwise, x □ y = y * x * x.
The precedence of operations: □ > ** > * = / = % = ☆ > + = -。
Parentheses have the highest priority, and the expression i... | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 □ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": ... |
logic-v2 | Define □, the rules are as follows:
on the real number field, x □ y = y * abs(y ** y) + x.
and ▽, 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 parenthese... | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 % 7 ▽ 10 □ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting... |
logic-v2 | Define ◇, the rules are as follows:
when y is a multiple of 5, x ◇ y = y * x + x;
otherwise, x ◇ y = 3 + 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": "22",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ◇ 8 * 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dep... |
logic-v2 | Define ⊗, the rules are as follows:
on the real number field, x ⊗ y = (x + y) - x + y - 5.
and ⊕, the rules are as follows:
when y is a multiple of 3, x ⊕ y = y * x - x - 3 ** y;
otherwise, x ⊕ y = 4 - x + 2 + 5 - y.
and ○, the rules are as follows:
on the real number field, x ○ y = y / x.
The precedence of ope... | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ⊕ 6 ○ 7 ⊗ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_... |
logic-v2 | 定义 ○，规则如下：
实数域上，x ○ y = y + y * x * y。
和 △，规则如下：
实数域上，x △ y = x * y * y。
和 □，规则如下：
当x是偶数时，x □ y = y - x + x * y；
其他情况下，x □ y = 5 ○ 2 / y ** x。
运算优先级：△ > ○ = □ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5 □ 8 / 7 ○ 1 △ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1e-06",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 □ 8 / 7 ○ 1 △ 3",
"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 = 4 * y - x - y.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = (y ⊕ y) * x / x.
and ☆, the rules are as follows:
on the real number field, x ☆ y = x * y / x.
The precedence of operations: ☆ > ** > * = / = % = ⊕ > + = - = ⊗。
P... | {
"game_data": {
"answer": "24",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ☆ 3 ⊗ 6 ⊕ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting... |
logic-v2 | 定义 ⊕，规则如下：
实数域上，x ⊕ y = x * y / (y)。
和 ○，规则如下：
实数域上，x ○ y = y - x * x + y。
和 ♢，规则如下：
实数域上，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: 4 ♢ 8 ○ 3 ○ 1 ⊕ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-0.004759",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ♢ 8 ○ 3 ○ 1 ⊕ 2",
"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 even, x ⊙ y = x + x + y * 3;
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: 6 ⊙ 9... | {
"game_data": {
"answer": "-27",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ⊙ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth"... |
logic-v2 | 定义 □，规则如下：
实数域上，x □ y = x * 2 - 2 / x - y。
和 ◎，规则如下：
实数域上，x ◎ y = x □ (x + y + x + y)。
和 ☆，规则如下：
实数域上，x ☆ y = y ◎ y / y - x + 4。
运算优先级：□ = ◎ > ** > * = / = % = ☆ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 □ 8 ☆ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-1.707483",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 □ 8 ☆ 7",
"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5的倍数时，x □ y = x * y - y；
其他情况下，x □ y = 5 + y - 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: 1 ▽ 10 □ 1 - 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ▽ 10 □ 1 - 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 + x。
和 ⊙，规则如下：
当x和y的和是奇数时，x ⊙ y = x - x - y；
其他情况下，x ⊙ y = (y) * y - x。
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 + 3 ♡ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "48",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ⊙ 7 + 3 ♡ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting... |
logic-v2 | Define ◎, the rules are as follows:
on the real number field, x ◎ y = x + y * y + x - x.
and ♡, the rules are as follows:
on the real number field, x ♡ y = y * x + 2.
The precedence of operations: ◎ = ♡ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is cal... | {
"game_data": {
"answer": "93",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ◎ 3 ♡ 8 - 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting... |
logic-v2 | 定义 ⊙，规则如下：
当x和y都是偶数时，x ⊙ y = x / y；
其他情况下，x ⊙ y = y + y - x。
和 □，规则如下：
实数域上，x □ y = y + x。
和 ○，规则如下：
实数域上，x ○ y = x * 1 / 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 □ 9 ○ 4 ⊙ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-6.25",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 □ 9 ○ 4 ⊙ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nes... |
logic-v2 | Define ◇, the rules are as follows:
when the sum of x and y is odd, x ◇ y = y - y + y * x;
otherwise, x ◇ y = 2 - 5 * y + x.
The precedence of operations: ◇ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of t... | {
"game_data": {
"answer": "8000",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ◇ 5 ** 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小于y时，x ◇ y = x * x / y * y；
其他情况下，x ◇ y = y * x + 4 - 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: 4 ◇ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "16",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ◇ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth":... |
logic-v2 | 定义 ☆，规则如下：
实数域上，x ☆ y = x - x + y * x + x。
和 ♢，规则如下：
当x等于y时，x ♢ y = x - x / 3 + y - y；
其他情况下，x ♢ y = x / y。
运算优先级：☆ > ♢ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 / 4 ♢ 3 ☆ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 / 4 ♢ 3 ☆ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_... |
logic-v2 | 定义 ☆，规则如下：
实数域上，x ☆ y = y * x * y。
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: 5 ○ 3 ☆ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "22500",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ○ 3 ☆ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_... |
logic-v2 | 定义 □，规则如下：
当x和y都是偶数时，x □ y = abs(y) * x；
其他情况下，x □ y = y * y + x。
和 ◇，规则如下：
当x是3的倍数时，x ◇ y = x + y + x；
其他情况下，x ◇ y = x + 2 + y。
运算优先级：◇ > □ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 9 □ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "45",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 □ 6",
"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 - y / x / x.
and ⊕, the rules are as follows:
when the sum of x and y is even, x ⊕ y = y - y * y * x;
otherwise, x ⊕ y = y ♡ 3 + x * x.
The precedence of operations: ⊕ > ** > * = / = % > + = - = ♡。
Parentheses have the highest priority, and t... | {
"game_data": {
"answer": "8.888889",
"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_d... |
logic-v2 | Define ♡, the rules are as follows:
when x and y are both even, x ♡ y = x * x + y;
otherwise, x ♡ y = abs(y * y + 1) - x * 2.
and □, the rules are as follows:
on the real number field, x □ y = y * x ** 1.
and ○, the rules are as follows:
when x is greater than y, x ○ y = y * x + x + y;
otherwise, x ○ y = x * ... | {
"game_data": {
"answer": "57424",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ○ 9 □ 1 ♡ 3 ○ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"... |
logic-v2 | 定义 ♢，规则如下：
实数域上，x ♢ y = x * y + x - 1。
和 ◎，规则如下：
当x大于y时，x ◎ y = y * x ** 1；
其他情况下，x ◎ y = y + x + (y + 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: 6 - 9 ♢ 1 ◇ 5 ◎ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-3054",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 - 9 ♢ 1 ◇ 5 ◎ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"... |
logic-v2 | Define ▽, the rules are as follows:
on the real number field, x ▽ y = x * y - 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 * 10 ▽ 6
Please fill your... | {
"game_data": {
"answer": "-268",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 - 5 * 10 ▽ 6",
"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都是偶数时，x ⊗ y = x + y；
其他情况下，x ⊗ y = y * y - x。
和 ○，规则如下：
当x是奇数时，x ○ y = x ⊗ y；
其他情况下，x ○ y = x + x / y。
和 ⊕，规则如下：
当x和y的和是偶数时，x ⊕ y = x * 5 ○ 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: 10 ○ 1 ⊗ 10 ⊕ 2 + 10 * 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "80.001778",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ○ 1 ⊗ 10 ⊕ 2 + 10 * 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": nu... |
logic-v2 | 定义 ♢，规则如下：
当y是奇数时，x ♢ y = 2 - x - y - x - 4；
其他情况下，x ♢ y = x - (y - y + 1)。
和 ▽，规则如下：
实数域上，x ▽ y = y ** y ♢ x * y。
和 □，规则如下：
实数域上，x □ y = 4 - x * 3 * 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 ▽ 6 ♢ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "19",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ▽ 6 ♢ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_de... |
logic-v2 | 定义 ⊙，规则如下：
实数域上，x ⊙ y = 1 ** x + y。
和 ◇，规则如下：
当x等于y时，x ◇ y = y + x；
其他情况下，x ◇ y = y - 3 + x。
和 ⊗，规则如下：
当x等于y时，x ⊗ y = y / (x) * 4；
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 ⊗ 2 ◇ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "7",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ⊙ 9 ⊗ 2 ◇ 8",
"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 = y + 1 / y + x;
otherwise, x ♢ y = 2 - y * 5 * x.
and ○, the rules are as follows:
on the real number field, x ○ y = y * x - x ♢ y + 4.
and ◇, the rules are as follows:
on the real number field, x ◇ y = y * y + y - x.
The precedence of operations: ◇ > ♢ ... | {
"game_data": {
"answer": "-1528",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ♢ 8 ◇ 10",
"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 = y + x + x；
其他情况下，x ▽ y = x + x + y。
运算优先级：▽ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 ▽ 10 ** 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "27000",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ▽ 10 ** 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesti... |
logic-v2 | Define ◇, the rules are as follows:
on the real number field, x ◇ y = y / y / y * x * 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 expression: 7 ◇ 9 ◇ 8 ◇ 10
Please f... | {
"game_data": {
"answer": "1.215278",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ◇ 9 ◇ 8 ◇ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"... |
logic-v2 | 定义 ♢，规则如下：
实数域上，x ♢ y = x * y - x + y。
和 ○，规则如下：
实数域上，x ○ y = x - 5 / y。
和 ⊙，规则如下：
实数域上，x ⊙ y = x - (y) ○ y。
运算优先级：** > * = / = % = ⊙ > + = - = ♢ = ○。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7 ♢ 1 ○ 4 ○ 10 ⊙ 3 ♢ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-0.125",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ♢ 1 ○ 4 ○ 10 ⊙ 3 ♢ 7",
"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都是偶数时，x ◎ y = y + x；
其他情况下，x ◎ y = x - y * y。
和 ▽，规则如下：
实数域上，x ▽ y = y * y ** x。
运算优先级：◎ > ** > * = / = % > + = - = ▽。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 9 ** 9 ◎ 10 ▽ 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 ** 9 ◎ 10 ▽ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nestin... |
logic-v2 | Define ☆, the rules are as follows:
on the real number field, x ☆ y = y + y - y * x + y.
and ▽, the rules are as follows:
on the real number field, x ▽ y = y ☆ y - x.
The precedence of operations: ☆ > ** > * = / = % > + = - = ▽。
Parentheses have the highest priority, and the expression inside the parentheses is cal... | {
"game_data": {
"answer": "8",
"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 | 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: 2 △ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 △ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": ... |
logic-v2 | Define △, the rules are as follows:
when y is a multiple of 5, x △ y = x + y * y * x;
otherwise, x △ y = y * x - x - x.
The precedence of operations: ** = △ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the ex... | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ** 5 △ 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大于y时，x ♡ y = x - x * y + y - abs(y)；
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 + 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 ♡ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-14",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ⊗ 7 ♡ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_d... |
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: 6 ▽ 9 ** 9 % 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ▽ 9 ** 9 % 4",
"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 / x；
其他情况下，x ⊗ y = y + x。
和 ◎，规则如下：
实数域上，x ◎ y = (y + x)。
和 ♢，规则如下：
当x等于y时，x ♢ y = 3 * x + y；
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 ◎ 8 ♢ 1 ⊗ 6 ♢ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "71",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ◎ 8 ♢ 1 ⊗ 6 ♢ 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 = (y + x) * y.
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 = 3 / x - y.
The precedence of operations: ◎ > ** > * = / = % = ⊙ > + = - = ♢。
Parentheses h... | {
"game_data": {
"answer": "-341.666667",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ♢ 1 ⊙ 3 ◎ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
... |
logic-v2 | 定义 ♢，规则如下：
实数域上，x ♢ y = y / (x) * y。
和 ◇，规则如下：
当y是奇数时，x ◇ y = y - x ♢ y；
其他情况下，x ◇ y = x - (y ** y)。
和 ◎，规则如下：
当x小于y时，x ◎ y = x ◇ y；
其他情况下，x ◎ y = x * y。
运算优先级：◎ > ** = ◇ > * = / = % = ♢ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 9 ◎ 8 ♢ 6 ◇ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0.018904",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ◎ 8 ♢ 6 ◇ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"n... |
logic-v2 | 定义 ○，规则如下：
实数域上，x ○ y = x + 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
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "3",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3",
"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 the sum of x and y is odd, x ⊗ y = y * 3 ** abs(x) - y;
otherwise, x ⊗ y = x + y - x.
and ○, the rules are as follows:
on the real number field, x ○ y = x + y + 1 - y.
and ☆, the rules are as follows:
on the real number field, x ☆ y = y * x.
The precedence of operations:... | {
"game_data": {
"answer": "8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ⊗ 4 * 1 ○ 7 ☆ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nest... |
logic-v2 | Define ♢, the rules are as follows:
when x is even, x ♢ y = x + y + x - y;
otherwise, x ♢ y = x * (y * 4 - x) + y.
and ◎, the rules are as follows:
when x is a multiple of 5, x ◎ y = (3 ♢ y) - x;
otherwise, x ◎ y = x * x * y ♢ x ** y.
and □, the rules are as follows:
on the real number field, x □ y = y - x - ... | {
"game_data": {
"answer": "14",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ♢ 2 □ 4 ◎ 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 is a multiple of 5, x ☆ y = x + x + y;
otherwise, x ☆ y = y ** x.
and □, the rules are as follows:
on the real number field, x □ y = 4 + abs(y) / x.
The precedence of operations: ☆ > □ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression in... | {
"game_data": {
"answer": "-3.666667",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ☆ 9 □ 4 / 3 - 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
... |
logic-v2 | Define ⊙, the rules are as follows:
on the real number field, x ⊙ y = x / y ** x + y / y.
and ☆, the rules are as follows:
on the real number field, x ☆ y = x - x + x * y.
and △, the rules are as follows:
on the real number field, x △ y = x * y + (y).
The precedence of operations: △ > ** = ⊙ > * = / = % = ☆ > + =... | {
"game_data": {
"answer": "53.999485",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 △ 2 / 10 ⊙ 4 ☆ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
... |
logic-v2 | 定义 ◎，规则如下：
实数域上，x ◎ y = 5 + x / y。
和 ⊗，规则如下：
当x是奇数时，x ⊗ y = y * (x) - y；
其他情况下，x ⊗ y = 5 * abs(x * y)。
运算优先级：** > * = / = % = ◎ > + = - = ⊗。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 ⊗ 6 * 2 ◎ 7 + 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "139.285714",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ⊗ 6 * 2 ◎ 7 + 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
... |
logic-v2 | Define ⊗, the rules are as follows:
on the real number field, x ⊗ y = x + x + y.
and ◎, the rules are as follows:
on the real number field, x ◎ y = x ⊗ y + y.
and ♢, the rules are as follows:
when y is odd, x ♢ y = 1 ⊗ y ** x;
otherwise, x ♢ y = x + y ⊗ 1.
The precedence of operations: ** = ♢ > * = / = % = ◎ > ... | {
"game_data": {
"answer": "50",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ♢ 2 ⊗ 9 ◎ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting... |
logic-v2 | 定义 ♢，规则如下：
当x是3的倍数时，x ♢ y = (x + 2 / 1) * 1 + y；
其他情况下，x ♢ y = x - y + 3 * y - y。
和 ◎，规则如下：
当x和y的和是奇数时，x ◎ y = y * 5 * 2 - 5 ♢ x；
其他情况下，x ◎ y = (y + y + x ♢ x) * y。
和 ⊗，规则如下：
当x和y的和是偶数时，x ⊗ y = x - y * y * y - y；
其他情况下，x ⊗ y = y + x * x * x / y。
运算优先级：◎ = ⊗ > ** > * = / = % > + = - = ♢。
括号具有最高优先级，先计算括号内的表达式... | {
"game_data": {
"answer": "356.555556",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ⊗ 9 ◎ 7 ♢ 8 ◎ 3",
"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 * x * x - y。
和 ⊗，规则如下：
当x是3的倍数时，x ⊗ y = x / 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: 2 % 1 ⊗ 2 □ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 % 1 ⊗ 2 □ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_... |
logic-v2 | Define ⊕, the rules are as follows:
on the real number field, x ⊕ y = x + y + y.
and □, the rules are as follows:
when x is less than y, x □ y = y + y * x;
otherwise, x □ y = y ⊕ y * x.
and ⊗, the rules are as follows:
when y is odd, x ⊗ y = x + (x + y);
otherwise, x ⊗ y = y - x * x.
The precedence of operati... | {
"game_data": {
"answer": "-564",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 □ 8 ⊗ 8 ⊕ 2",
"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 5, x ♡ y = y + 3 + x - y + x;
otherwise, x ♡ y = x * y + y + x + x.
and □, the rules are as follows:
on the real number field, x □ y = (y - y + x) * y / y.
The precedence of operations: □ > ** = ♡ > * = / = % > + = -。
Parentheses have the highest priorit... | {
"game_data": {
"answer": "48",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ♡ 8 □ 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:
on the real number field, x ◎ y = x + y / 4.
and ⊙, the rules are as follows:
when y is even, x ⊙ y = x ◎ y + y;
otherwise, x ⊙ y = x / y + y.
The precedence of operations: ◎ > ⊙ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the pare... | {
"game_data": {
"answer": "5.142857",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ⊙ 8 / 3 ◎ 2 % 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
... |
logic-v2 | Define ▽, the rules are as follows:
on the real number field, x ▽ y = 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: 8 ▽ 1
Please fill your final an... | {
"game_data": {
"answer": "65",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ▽ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth":... |
logic-v2 | 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
Please fill your final answer... | {
"game_data": {
"answer": "5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null... |
logic-v2 | Define ♢, the rules are as follows:
when y is a multiple of 3, x ♢ y = x + y * x;
otherwise, x ♢ y = y * abs(x).
and ⊙, the rules are as follows:
when y is a multiple of 3, x ⊙ y = y * x * y;
otherwise, x ⊙ y = (x ** 2 / y).
and ○, the rules are as follows:
on the real number field, x ○ y = y / x * x.
The pre... | {
"game_data": {
"answer": "0.833333",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ⊙ 6 ○ 6 ♢ 5",
"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 - 1.
and ◇, 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 ... | {
"game_data": {
"answer": "1.25",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ◇ 3 ◎ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_d... |
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