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logic-v2
Define ♡, the rules are as follows: when the sum of x and y is odd, x ♡ y = 2 + x * y; otherwise, x ♡ y = (x + y - y). and ◎, the rules are as follows: on the real number field, x ◎ y = y * x * (y). The precedence of operations: ◎ > ** = ♡ > * = / = % > + = -。 Parentheses have the highest priority, and the expres...
{ "game_data": { "answer": "20", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "6 ♡ 3", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "nesting_depth":...
logic-v2
Define ⊙, the rules are as follows: on the real number field, x ⊙ y = y + x. and ▽, 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 / 4) ▽ y. The precedence of operations: ** = ♡ > * = / = % = ▽ > + = - = ⊙。 Parentheses h...
{ "game_data": { "answer": "30.5", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "6 ▽ 9 ♡ 5", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "nesting_d...
logic-v2
定义 ◎,规则如下: 当x是5的倍数时,x ◎ y = abs(y * x) * 5; 其他情况下,x ◎ y = x * x * y。 和 □,规则如下: 实数域上,x □ y = (x / y) ◎ y。 运算优先级:◎ = □ > ** > * = / = % > + = -。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 3 ◎ 8 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "72", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "3 ◎ 8", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nesting_depth":...
logic-v2
Define ⊙, the rules are as follows: when the sum of x and y is even, x ⊙ y = x - abs(y) * 2; otherwise, x ⊙ y = (4 - y * 3 + x). and ◎, the rules are as follows: on the real number field, x ◎ y = x * x - y. and ○, the rules are as follows: on the real number field, x ○ y = x - x - y - y. The precedence of opera...
{ "game_data": { "answer": "23", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "7 ⊙ 1 ◎ 2", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "nesting_dep...
logic-v2
Define ⊗, the rules are as follows: when x and y are both odd, x ⊗ y = y + x - 1 * y; otherwise, x ⊗ y = x + y + y * y + x. and ♢, the rules are as follows: when x is even, x ♢ y = y * x * y; otherwise, x ♢ y = x / x / y - x * x. The precedence of operations: ⊗ > ** = ♢ > * = / = % > + = -。 Parentheses have the...
{ "game_data": { "answer": "21376", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "6 ⊗ 10 ⊗ 9 ♢ 8", "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 a multiple of 3, x ⊗ y = x - y * x + x; otherwise, x ⊗ y = (x - y - y) * x - x. and ◎, the rules are as follows: when the sum of x and y is odd, x ◎ y = x ⊗ x - y + x * x; otherwise, x ◎ y = x ⊗ y * x - y + y. The precedence of operations: ⊗ > ** > * = / = % = ◎ > +...
{ "game_data": { "answer": "0", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "3 % 10 ⊗ 4 ◎ 1", "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 + 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: 9 ▽ 8 % 4 ☆ 8 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "7", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "9 ▽ 8 % 4 ☆ 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 x is a multiple of 3, x ⊗ y = y / y / x - x ** x; otherwise, x ⊗ y = x - x - y - y - x. and ▽, the rules are as follows: when x is odd, x ▽ y = x - y / y ⊗ y; otherwise, x ▽ y = x ** 3 + 3 + y - x. and ⊙, the rules are as follows: when x is equal to y, x ⊙ y = 4 ⊗ y * ...
{ "game_data": { "answer": "-2006", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "2 ⊙ 1 ⊗ 10 ▽ 8", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "nes...
logic-v2
Define ▽, the rules are as follows: when x is a multiple of 5, x ▽ y = x + x * y + x + y; otherwise, x ▽ y = x / 5 + y / x. The precedence of operations: ** > * = / = % > + = - = ▽。 Parentheses have the highest priority, and the expression inside the parentheses is calculated first. Please calculate the value of th...
{ "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: on the real number field, x ☆ y = abs(y + y) + x. and ▽, the rules are as follows: on the real number field, x ▽ y = x + y ☆ (y + 2). The precedence of operations: ** = ▽ > * = / = % = ☆ > + = -。 Parentheses have the highest priority, and the expression inside the parentheses is ...
{ "game_data": { "answer": "76", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "6 ▽ 10 ▽ 8 ☆ 4", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "nestin...
logic-v2
Define □, the rules are as follows: when the sum of x and y is even, x □ y = x * y - y; otherwise, x □ y = y - x + y. and ⊙, the rules are as follows: on the real number field, x ⊙ y = x * y + y. The precedence of operations: ** = ⊙ > * = / = % = □ > + = -。 Parentheses have the highest priority, and the expressio...
{ "game_data": { "answer": "280", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "8 □ 7 ⊙ 5", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "nesting_de...
logic-v2
Define ▽, the rules are as follows: when x is even, x ▽ y = x * 1 ** y / y / x; otherwise, x ▽ y = (x + x - 5 - x * y). The precedence of operations: ▽ > ** > * = / = % > + = -。 Parentheses have the highest priority, and the expression inside the parentheses is calculated first. Please calculate the value of the ex...
{ "game_data": { "answer": "0.125", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "6 ▽ 8 ** 6 ▽ 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 = (x) * x - 4 + 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 / 10 ◇ 3 % 2 Please...
{ "game_data": { "answer": "0.058252", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "6 / 10 ◇ 3 % 2", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "...
logic-v2
定义 ◇,规则如下: 当x大于y时,x ◇ y = x * y + x + x; 其他情况下,x ◇ y = (4 + y) - x + y。 运算优先级:** = ◇ > * = / = % > + = -。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 8 ◇ 2 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "32", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "8 ◇ 2", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nesting_depth":...
logic-v2
定义 ○,规则如下: 实数域上,x ○ y = y * (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 ○ 8 / 2 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "28", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "2 ○ 8 / 2", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nesting_dep...
logic-v2
Define △, the rules are as follows: when x is a multiple of 3, x △ y = x + x + abs(y); otherwise, x △ y = x * abs(y). The precedence of operations: △ > ** > * = / = % > + = -。 Parentheses have the highest priority, and the expression inside the parentheses is calculated first. Please calculate the value of the expr...
{ "game_data": { "answer": "2", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "2 △ 2 * 8 % 10", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "nesting...
logic-v2
Define ♡, the rules are as follows: when x is greater than y, x ♡ y = y / y * y * y - x; otherwise, x ♡ y = x * x + y / y. and ◎, the rules are as follows: when x and y are both even, x ◎ y = x / y; otherwise, x ◎ y = x * y ♡ y * y + y. The precedence of operations: ♡ > ** > * = / = % > + = - = ◎。 Parentheses h...
{ "game_data": { "answer": "5", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "2 ♡ 7", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "nesting_depth": ...
logic-v2
Define △, the rules are as follows: when x is equal to y, x △ y = y + 2 + x + 3; otherwise, x △ y = y * x. and ○, the rules are as follows: when y is even, x ○ y = 3 * 1 * y * x; otherwise, x ○ y = y △ x + y + y. The precedence of operations: △ = ○ > ** > * = / = % > + = -。 Parentheses have the highest priority...
{ "game_data": { "answer": "189", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "7 ○ 3 △ 7", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "nesting_de...
logic-v2
Define ○, the rules are as follows: on the real number field, x ○ y = y * x. The precedence of operations: ** = ○ > * = / = % > + = -。 Parentheses have the highest priority, and the expression inside the parentheses is calculated first. Please calculate the value of the expression: 3 ○ 3 ○ 3 Please fill your final an...
{ "game_data": { "answer": "27", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "3 ○ 3 ○ 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等于y时,x ☆ y = y * x - x ** y - y; 其他情况下,x ☆ y = (y - x - y + y * y)。 运算优先级:** = ☆ > * = / = % > + = -。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 2 ☆ 4 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "14", "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
定义 ♡,规则如下: 当x和y的和是奇数时,x ♡ y = 3 ** y + 2 * x + x; 其他情况下,x ♡ y = y + y - x + y * x。 和 ☆,规则如下: 当x大于y时,x ☆ y = abs(x * y) + x / x + y; 其他情况下,x ☆ y = y + x - x + x + x。 运算优先级:♡ = ☆ > ** > * = / = % > + = -。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 3 ♡ 8 ☆ 9 + 7 ☆ 3 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "59165", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "3 ♡ 8 ☆ 9 + 7 ☆ 3", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "...
logic-v2
定义 ▽,规则如下: 当x和y的和是偶数时,x ▽ y = y - y + x; 其他情况下,x ▽ y = 5 - (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 ▽ 8 / 5 ** 2 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "0.32", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "8 ▽ 8 / 5 ** 2", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nest...
logic-v2
定义 ◎,规则如下: 实数域上,x ◎ y = y - y + x。 和 ⊕,规则如下: 当x是偶数时,x ⊕ y = x + y - abs(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: 8 ◎ 9 % 3 ⊕ 2 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "8", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "8 ◎ 9 % 3 ⊕ 2", "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 * x + y / x. and ⊙, the rules are as follows: when x is equal to y, x ⊙ y = x + y + y + y - 4; otherwise, x ⊙ y = y - x - (x + x). and ○, the rules are as follows: on the real number field, x ○ y = x ▽ (y) - y. The precedence of operati...
{ "game_data": { "answer": "0.118694", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "10 / 10 ▽ 2 ○ 1 ⊙ 2 ⊙ 3", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null...
logic-v2
定义 ◎,规则如下: 当x和y的和是奇数时,x ◎ y = x + x + y; 其他情况下,x ◎ y = y - y * x。 和 ▽,规则如下: 实数域上,x ▽ y = x * (y) * 4。 运算优先级:** = ▽ > * = / = % > + = - = ◎。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 1 ▽ 3 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "12", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "1 ▽ 3", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nesting_depth":...
logic-v2
定义 ⊕,规则如下: 当x大于y时,x ⊕ y = x + y; 其他情况下,x ⊕ y = x * y。 和 ♢,规则如下: 实数域上,x ♢ y = 2 * y - x。 和 ⊙,规则如下: 当x大于y时,x ⊙ 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: 9 ⊕ 5 ♢ 1 ⊙ 7 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "5.142857", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "9 ⊕ 5 ♢ 1 ⊙ 7", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "n...
logic-v2
Define ♡, the rules are as follows: on the real number field, x ♡ y = y - y + y * x. and ▽, the rules are as follows: when y is even, x ▽ y = (x - x + y) - 2; otherwise, x ▽ y = x + y * 1 * 5. The precedence of operations: ** = ♡ = ▽ > * = / = % > + = -。 Parentheses have the highest priority, and the expression i...
{ "game_data": { "answer": "70", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "7 ♡ 10", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "nesting_depth"...
logic-v2
定义 ⊗,规则如下: 实数域上,x ⊗ y = abs(x + y + 1 - y)。 和 ☆,规则如下: 当x是偶数时,x ☆ y = y + x + abs(1 ** y / y); 其他情况下,x ☆ y = x * y + (y) - y。 和 ⊕,规则如下: 当x和y的和是偶数时,x ⊕ y = x ⊗ x * y; 其他情况下,x ⊕ y = 3 * 1 + y / x。 运算优先级:☆ = ⊕ > ** > * = / = % = ⊗ > + = -。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 9 ☆ 5 ⊗ 10 ⊕ 2 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "46", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "9 ☆ 5 ⊗ 10 ⊕ 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 x is odd, x △ y = 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: 7 △ 1 Please f...
{ "game_data": { "answer": "8", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "7 △ 1", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "nesting_depth": ...
logic-v2
定义 △,规则如下: 当x大于y时,x △ y = x / y + x; 其他情况下,x △ y = x + y - y。 和 ☆,规则如下: 实数域上,x ☆ y = y + x △ 1。 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: 3 ⊙ 6 ☆ 6 △ 2 △ 10 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "48", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "3 ⊙ 6 ☆ 6 △ 2 △ 10", "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 = y * x - x + y。 和 ☆,规则如下: 当y是奇数时,x ☆ y = y - (y * x - y); 其他情况下,x ☆ y = y ◎ 3 + 1 * x。 运算优先级:** = ☆ > * = / = % > + = - = ◎。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 10 ◎ 2 ☆ 10 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "265", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "10 ◎ 2 ☆ 10", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nesting_...
logic-v2
定义 ♢,规则如下: 当y是3的倍数时,x ♢ y = y + y * x; 其他情况下,x ♢ y = abs(x - y) + x。 和 ☆,规则如下: 实数域上,x ☆ y = y / x ♢ y + 4 + x。 和 ◇,规则如下: 当y是5的倍数时,x ◇ y = x / y ☆ x - 4 / x; 其他情况下,x ◇ y = y - x ♢ x / y * x。 运算优先级:◇ > ** > * = / = % = ♢ > + = - = ☆。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 10 ♢ 10 ◇ 2 ☆ 4 % 5 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "76", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "10 ♢ 10 ◇ 2 ☆ 4 % 5", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "n...
logic-v2
定义 △,规则如下: 实数域上,x △ y = y - x - 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: 7 △ 2 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "-6.428571", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "7 △ 2", "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 + 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: 4 ▽ 4 ▽ 5 / 6 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "-0.333333", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "4 ▽ 4 ▽ 5 / 6", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "...
logic-v2
Define ♡, the rules are as follows: on the real number field, x ♡ y = y * x. and □, the rules are as follows: when x and y are both even, x □ y = 3 + y + x; otherwise, x □ y = y + x. The precedence of operations: ♡ > ** = □ > * = / = % > + = -。 Parentheses have the highest priority, and the expression inside the ...
{ "game_data": { "answer": "5", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "5 % 6 □ 7 ♡ 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 * x。 和 ▽,规则如下: 实数域上,x ▽ y = 4 + y + x。 和 ♡,规则如下: 实数域上,x ♡ y = x - y ▽ x。 运算优先级:♡ > ** > * = / = % = ⊙ = ▽ > + = -。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 6 ▽ 2 ⊙ 7 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "-72", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "6 ▽ 2 ⊙ 7", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nesting_de...
logic-v2
定义 ○,规则如下: 当x和y的和是奇数时,x ○ y = y - x - y; 其他情况下,x ○ y = y ** y - x。 运算优先级:** > * = / = % > + = - = ○。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 2 ○ 3 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "-2", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "2 ○ 3", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nesting_depth":...
logic-v2
Define ♡, the rules are as follows: when x is a multiple of 5, x ♡ y = y + x * 4 + x; otherwise, x ♡ y = 5 * x + abs(y). and ♢, the rules are as follows: when y is a multiple of 3, x ♢ y = x * 4 + y + x; otherwise, x ♢ y = (y * y / x - y). The precedence of operations: ♢ > ** > * = / = % > + = - = ♡。 Parenthese...
{ "game_data": { "answer": "36", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "6 ♡ 6", "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 * x - 3; otherwise, x ♡ y = y - (x * y). and ⊕, the rules are as follows: on the real number field, x ⊕ y = y ** 4 + abs(x / x). The precedence of operations: ⊕ > ** > * = / = % > + = - = ♡。 Parentheses have the highest priority, and the expr...
{ "game_data": { "answer": "17", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "7 ⊕ 2", "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 = abs(y - x) - x * y。 和 ◎,规则如下: 当x是奇数时,x ◎ y = 5 - y + y + 2 * x; 其他情况下,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 ◎ 9 * 10 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "-64810", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "9 ♡ 10 ◎ 9 * 10", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "n...
logic-v2
Define △, the rules are as follows: on the real number field, x △ y = y + x - x ** 1 ** y. The precedence of operations: △ > ** > * = / = % > + = -。 Parentheses have the highest priority, and the expression inside the parentheses is calculated first. Please calculate the value of the expression: 5 Please fill your fi...
{ "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
定义 ⊕,规则如下: 当x和y的和是奇数时,x ⊕ y = abs(y) / x; 其他情况下,x ⊕ y = x / y ** y。 和 ♡,规则如下: 实数域上,x ♡ y = y - x * y。 和 ♢,规则如下: 当x是奇数时,x ♢ y = y * x; 其他情况下,x ♢ y = x * y。 运算优先级:⊕ > ♡ = ♢ > ** > * = / = % > + = -。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 1 ♡ 2 ♢ 1 ⊕ 2 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "0", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "1 ♡ 2 ♢ 1 ⊕ 2", "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 = 5 - x / x * y。 和 △,规则如下: 实数域上,x △ y = x * y / y * 4。 和 ◇,规则如下: 当x等于y时,x ◇ y = 4 ♢ y * y - x; 其他情况下,x ◇ y = y ♢ y - y - x。 运算优先级:** = ♢ = ◇ > * = / = % = △ > + = -。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 2 △ 9 ◇ 3 ♢ 2 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "8", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "2 △ 9 ◇ 3 ♢ 2", "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 = 4 * x - 4 - y. 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 expression inside the parentheses is cal...
{ "game_data": { "answer": "2", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "9 ♡ 6 △ 1 % 8", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "nesting_...
logic-v2
Define ◇, the rules are as follows: when x and y are both odd, x ◇ y = y + x + 4; otherwise, x ◇ y = y + x. The precedence of operations: ** > * = / = % = ◇ > + = -。 Parentheses have the highest priority, and the expression inside the parentheses is calculated first. Please calculate the value of the expression: 4 ...
{ "game_data": { "answer": "9", "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
定义 ♢,规则如下: 实数域上,x ♢ y = x * y * x。 和 △,规则如下: 当x和y都是奇数时,x △ y = x * (y - y + x); 其他情况下,x △ y = x * y + 2 ** y。 和 □,规则如下: 实数域上,x □ y = x * y △ y + y。 运算优先级:♢ = △ > ** > * = / = % > + = - = □。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 7 △ 7 □ 2 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "394", "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_de...
logic-v2
Define ▽, the rules are as follows: when the sum of x and y is odd, x ▽ y = x - x * y + y - y; otherwise, x ▽ y = abs(x) * y - x * y * 3. The precedence of operations: ** = ▽ > * = / = % > + = -。 Parentheses have the highest priority, and the expression inside the parentheses is calculated first. Please calculate t...
{ "game_data": { "answer": "10", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "10 + 6 ▽ 1", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "nesting_de...
logic-v2
定义 ⊙,规则如下: 实数域上,x ⊙ y = x / y * y - 5。 和 ▽,规则如下: 实数域上,x ▽ y = y ** y - x * x。 和 ♢,规则如下: 当x小于y时,x ♢ y = x ⊙ (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: 9 - 10 ⊙ 8 ♢ 6 ▽ 7 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "-6", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "9 - 10 ⊙ 8 ♢ 6 ▽ 7", "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 = y - 2 + y ** (x - 4)。 和 △,规则如下: 实数域上,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: 7 △ 3 ☆ 6 ☆ 3 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "84.211209", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "7 △ 3 ☆ 6 ☆ 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 = (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 % 6 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "1", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "2 △ 1 % 6", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nesting_dept...
logic-v2
定义 ♢,规则如下: 当x大于y时,x ♢ y = (x - y + y) * 4; 其他情况下,x ♢ y = y * x + y - x。 和 ○,规则如下: 实数域上,x ○ y = x ** y - abs(y - x)。 和 ◇,规则如下: 实数域上,x ◇ y = y - y ♢ x。 运算优先级:○ = ◇ > ** > * = / = % = ♢ > + = -。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 3 ◇ 6 ♢ 2 ♢ 6 ○ 4 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "-19394", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "3 ◇ 6 ♢ 2 ♢ 6 ○ 4", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, ...
logic-v2
Define ○, the rules are as follows: when x is a multiple of 5, x ○ y = y ** abs(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 expressi...
{ "game_data": { "answer": "32", "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 greater than y, x ⊕ y = y / x; otherwise, x ⊕ y = y + y - x. and ♡, the rules are as follows: when x and y are both even, x ♡ y = x - x / y ⊕ x; otherwise, x ♡ y = y ⊕ x * x / x. and ⊗, the rules are as follows: when x is even, x ⊗ y = (y) + y + y ♡ x; otherwise, ...
{ "game_data": { "answer": "30.8", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "10 ⊗ 4 ⊕ 10", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "nesting...
logic-v2
Define ♢, the rules are as follows: when x is less than y, x ♢ y = x + y + y * x; otherwise, x ♢ y = y * x. and ○, the rules are as follows: on the real number field, x ○ y = y * x / x + y. and ☆, the rules are as follows: when x and y are both even, x ☆ y = 2 ♢ y * x + x; otherwise, x ☆ y = y / x ** x. The p...
{ "game_data": { "answer": "0.0", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "7 ○ 4 ♢ 4 - 7 ☆ 3", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "ne...
logic-v2
Define ♡, the rules are as follows: when y is a multiple of 5, x ♡ y = x * 5 * y; otherwise, x ♡ y = x - (y) * x. 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 in...
{ "game_data": { "answer": "350", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "7 ♡ 10", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "nesting_depth...
logic-v2
定义 ⊕,规则如下: 实数域上,x ⊕ y = y - x * x。 和 ◇,规则如下: 当x是5的倍数时,x ◇ y = y ⊕ y ** y ** y / x; 其他情况下,x ◇ y = y - y - x + y ⊕ x。 和 ⊙,规则如下: 实数域上,x ⊙ y = x - x + x * y - (x)。 运算优先级:⊕ = ⊙ > ** = ◇ > * = / = % > + = -。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 5 ⊙ 9 ⊕ 7 ◇ 3 ⊙ 7 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "-324", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "5 ⊙ 9 ⊕ 7 ◇ 3 ⊙ 7", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "n...
logic-v2
Define ◎, the rules are as follows: on the real number field, x ◎ y = y / x + y. and ⊙, the rules are as follows: when x and y are both even, x ⊙ y = x * 4 * y; otherwise, x ⊙ y = x ◎ y. The precedence of operations: ** > * = / = % = ◎ = ⊙ > + = -。 Parentheses have the highest priority, and the expression inside ...
{ "game_data": { "answer": "7.583333", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "5 ⊙ 10 ◎ 7", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "nest...
logic-v2
Define ☆, the rules are as follows: on the real number field, x ☆ y = y - x - y + 5. and ♢, the rules are as follows: when y is odd, x ♢ y = 3 * y - x + y; otherwise, x ♢ y = (y + x - x). The precedence of operations: ♢ > ** > * = / = % = ☆ > + = -。 Parentheses have the highest priority, and the expression inside...
{ "game_data": { "answer": "8", "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: 实数域上,x △ y = x + (y / y)。 和 ♡,规则如下: 实数域上,x ♡ y = y △ 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: 6 ♡ 10 △ 2 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "24", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "6 ♡ 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 y is a multiple of 5, x ⊗ y = (x) / 1 + 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 expres...
{ "game_data": { "answer": "-546", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "10 * 3 - 9 ⊗ 8", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "nest...
logic-v2
定义 ⊙,规则如下: 实数域上,x ⊙ y = y + x。 和 ○,规则如下: 当x等于y时,x ○ y = x + y; 其他情况下,x ○ y = (4 / x) + 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: 5 ☆ 8 ○ 7 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "12.5", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "5 ☆ 8 ○ 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: 实数域上,x ○ y = x * 5 + y + x。 运算优先级:** > * = / = % = ○ > + = -。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 5 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "5", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "5", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nesting_depth": null...
logic-v2
定义 ◇,规则如下: 当x和y都是奇数时,x ◇ y = x * 2 ** y; 其他情况下,x ◇ y = 5 - 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: 3 ◇ 2 - 10 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "-14", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "3 ◇ 2 - 10", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nesting_d...
logic-v2
Define ⊕, the rules are as follows: on the real number field, x ⊕ y = x * x - x * y - x. and △, the rules are as follows: on the real number field, x △ y = x + y * 4 - y + 5. and ◇, the rules are as follows: on the real number field, x ◇ y = y * y + y + x + x. The precedence of operations: ** = △ > * = / = % > + ...
{ "game_data": { "answer": "4284", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "2 △ 2 ◇ 6 ⊕ 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x和y都是偶数时,x ♢ y = x * y * x; 其他情况下,x ♢ y = x + y / y。 和 ○,规则如下: 当x和y都是偶数时,x ○ y = abs(x) + y / x; 其他情况下,x ○ y = x * y。 和 △,规则如下: 实数域上,x △ y = y * y ○ x。 运算优先级:♢ > ** = △ > * = / = % > + = - = ○。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 5 △ 9 ♢ 2 ○ 6 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "3000", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "5 △ 9 ♢ 2 ○ 6", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nesti...
logic-v2
定义 ♡,规则如下: 当y是3的倍数时,x ♡ y = x / y; 其他情况下,x ♡ y = x / x * y。 和 ⊙,规则如下: 实数域上,x ⊙ y = x + x + y。 运算优先级:⊙ > ♡ > ** > * = / = % > + = -。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 5 ♡ 9 ⊙ 3 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "0.238095", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "5 ♡ 9 ⊙ 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 + abs(x / y). 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. The precedence of operations: ○ > ** > * = / = % = ⊙ > + = - = ♢。 Parenthese...
{ "game_data": { "answer": "9.125", "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, "nes...
logic-v2
Define ♢, the rules are as follows: when x is a multiple of 5, x ♢ y = y ** y / x - x + y; otherwise, x ♢ y = y - x * x * y / x. and ○, the rules are as follows: when x is a multiple of 5, x ○ y = x + y + x - x + 3; otherwise, x ○ y = x / x + y ♢ x / 3. and ◇, the rules are as follows: when x and y are both odd...
{ "game_data": { "answer": "-594", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "5 ○ 4 ♢ 3 ◇ 9", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "nesti...
logic-v2
Define ○, the rules are as follows: when x is a multiple of 3, x ○ y = x + 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: 9 ...
{ "game_data": { "answer": "18", "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
Define ⊙, the rules are as follows: when x and y are both odd, x ⊙ y = y / y * y + x * y; otherwise, x ⊙ y = (y + x / y + y). and ☆, the rules are as follows: when y is a multiple of 5, x ☆ y = (x) ** x + x * y; otherwise, x ☆ y = y + y * y - x + y. and ⊕, the rules are as follows: on the real number field, x ⊕...
{ "game_data": { "answer": "38.666667", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "1 ☆ 9 ⊙ 3 ⊕ 1", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "...
logic-v2
定义 ○,规则如下: 当y是3的倍数时,x ○ y = 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: 7 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "7", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "7", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nesting_depth": null...
logic-v2
Define ▽, the rules are as follows: when the sum of x and y is even, x ▽ y = x / x + y + x; otherwise, x ▽ y = x - y * x * x. The precedence of operations: ** > * = / = % = ▽ > + = -。 Parentheses have the highest priority, and the expression inside the parentheses is calculated first. Please calculate the value of ...
{ "game_data": { "answer": "-853", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "7 ▽ 6 * 3 ▽ 7", "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5的倍数时,x ◇ y = y + x - 2; 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: 6 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "6", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "6", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nesting_depth": null...
logic-v2
Define ⊙, the rules are as follows: on the real number field, x ⊙ y = y - y * (x * y). and △, the rules are as follows: on the real number field, x △ y = 3 - x * y ⊙ 4 - y. and ⊗, the rules are as follows: on the real number field, x ⊗ y = y △ 4 + x. The precedence of operations: ⊗ > ** = △ > * = / = % > + = - = ...
{ "game_data": { "answer": "75852", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "1 ⊗ 10 △ 8", "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 = abs(y + x + 2)。 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: 2 ♢ 8 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "56", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "2 ♢ 8", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nesting_depth":...
logic-v2
定义 ♢,规则如下: 当x和y都是奇数时,x ♢ y = x * x / x ** y - x; 其他情况下,x ♢ y = x + y。 和 ⊗,规则如下: 实数域上,x ⊗ y = y - y - x。 和 △,规则如下: 当x和y的和是偶数时,x △ y = x - 2 * y * y + y; 其他情况下,x △ y = y + x * x * 3 + y。 运算优先级:⊗ = △ > ♢ > ** > * = / = % > + = -。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 4 ⊗ 5 ♢ 7 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "3", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "4 ⊗ 5 ♢ 7", "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 = x + y * 3。 和 △,规则如下: 实数域上,x △ y = x + x * y。 和 ☆,规则如下: 实数域上,x ☆ y = 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 △ 4 ☆ 5 ⊕ 6 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "58", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "10 △ 4 ☆ 5 ⊕ 6", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nestin...
logic-v2
定义 ♢,规则如下: 实数域上,x ♢ y = y - y - x ** x。 和 △,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 ** 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 ○ 8 ♢ 3 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "0.037037", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "3 ○ 8 ♢ 3", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nesti...
logic-v2
Define △, the rules are as follows: when y is odd, x △ y = y + x - x; otherwise, x △ y = y - x * x * y. The precedence of operations: ** = △ > * = / = % > + = -。 Parentheses have the highest priority, and the expression inside the parentheses is calculated first. Please calculate the value of the expression: 10 - 4...
{ "game_data": { "answer": "70", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "10 - 4 △ 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和y都是奇数时,x ⊙ y = x - y * y - y - x; 其他情况下,x ⊙ y = y ** (2 - 1 - y) * x。 和 ♢,规则如下: 实数域上,x ♢ y = y ⊙ x * y * y。 和 ♡,规则如下: 当x和y都是偶数时,x ♡ y = y ♢ 2 * x - y; 其他情况下,x ♡ y = y - x / 1 - (y ⊙ x)。 运算优先级:♢ = ♡ > ** = ⊙ > * = / = % > + = -。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 7 ♢ 6 ⊙ 3 ♡ 10 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "0.0", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "7 ♢ 6 ⊙ 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: 当x是奇数时,x ⊙ y = y * x; 其他情况下,x ⊙ y = x / 2 - y。 和 ☆,规则如下: 实数域上,x ☆ y = x + (y + y)。 和 △,规则如下: 实数域上,x △ y = x * y。 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 ☆ 8 △ 8 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "72", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "2 ⊙ 8 ☆ 8 △ 8", "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 + 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 % 8 ◇ 1 - 8 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "-3", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "2 % 8 ◇ 1 - 8", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nesting...
logic-v2
Define ⊗, the rules are as follows: on the real number field, x ⊗ y = 2 * x * x * y * 2. and ▽, the rules are as follows: when the sum of x and y is odd, x ▽ y = x / x + y; otherwise, x ▽ y = (x + y - y * x) ⊗ y. and ♡, the rules are as follows: on the real number field, x ♡ y = abs(3) + x * y. The precedence o...
{ "game_data": { "answer": "577", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "8 ♡ 9 ▽ 6 ⊗ 4", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "nestin...
logic-v2
定义 □,规则如下: 当y是3的倍数时,x □ y = 5 ** x - y; 其他情况下,x □ y = 5 * y / x / 1。 和 ⊕,规则如下: 实数域上,x ⊕ y = x □ y * y * x。 运算优先级:□ > ** > * = / = % = ⊕ > + = -。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 9 ⊕ 6 □ 2 ⊕ 10 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "500.0", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "9 ⊕ 6 □ 2 ⊕ 10", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nes...
logic-v2
定义 ♡,规则如下: 实数域上,x ♡ y = x + y + x。 和 ◎,规则如下: 当x是奇数时,x ◎ y = x * x ♡ y; 其他情况下,x ◎ y = y + x。 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 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "28", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "9 ♡ 10", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nesting_depth"...
logic-v2
Define ⊕, the rules are as follows: when x is even, x ⊕ y = x - x ** y - y; otherwise, x ⊕ y = y - x - y. and △, the rules are as follows: when x is odd, x △ y = (x - x - y ⊕ y); otherwise, x △ y = 5 + x * 2 / y. and □, the rules are as follows: on the real number field, x □ y = (y - x) - x. The precedence of...
{ "game_data": { "answer": "7", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "5 ⊕ 5 □ 9 △ 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 - y. and △, the rules are as follows: when y is odd, x △ y = x ⊙ y * y; otherwise, x △ y = y + x. and ◇, the rules are as follows: on the real number field, x ◇ y = y △ x. The precedence of operations: ◇ > △ > ** = ⊙ > * = / = % > + = -...
{ "game_data": { "answer": "0", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "5 ⊙ 1 △ 2 ◇ 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 - 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 ○ 6 + 9 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "39", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "6 ○ 6 + 9", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nesting_dep...
logic-v2
定义 ♢,规则如下: 当y是5的倍数时,x ♢ y = x / y; 其他情况下,x ♢ y = y * y * x - x / x。 和 ⊗,规则如下: 实数域上,x ⊗ y = y ♢ x * x + y * y。 和 ◇,规则如下: 当x小于y时,x ◇ y = y * 5 ⊗ y * x - 3; 其他情况下,x ◇ y = y - x + y + y - y。 运算优先级:⊗ > ** = ◇ > * = / = % > + = - = ♢。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 2 ◇ 2 ⊗ 5 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "206", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "2 ◇ 2 ⊗ 5", "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 y is even, x △ y = y + x + x - y + x; otherwise, x △ y = 2 - 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 expressio...
{ "game_data": { "answer": "-19", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "6 △ 3", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "nesting_depth"...
logic-v2
定义 △,规则如下: 当y是3的倍数时,x △ y = y * x - y; 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 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "7", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "7", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nesting_depth": null...
logic-v2
Define ♢, the rules are as follows: when the sum of x and y is even, x ♢ y = x * 5 - y; otherwise, x ♢ y = y ** 3 * x. and ○, the rules are as follows: on the real number field, x ○ y = y / y + x. and ♡, the rules are as follows: when y is even, x ♡ y = x + x ♢ y; otherwise, x ♡ y = y * x ○ x. The precedence ...
{ "game_data": { "answer": "25", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "2 ♢ 6 ♡ 4 ○ 2", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "nesting...
logic-v2
Define ♢, the rules are as follows: on the real number field, x ♢ y = x + y. and ○, the rules are as follows: when x is odd, x ○ y = abs(y ** 2 + x); otherwise, x ○ y = x * y - x. and ♡, the rules are as follows: on the real number field, x ♡ y = 4 + abs(y * x). The precedence of operations: ♢ > ** > * = / = % ...
{ "game_data": { "answer": "312", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "8 ○ 2 ♢ 4 ♡ 6", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "nestin...
logic-v2
定义 ▽,规则如下: 当y是5的倍数时,x ▽ y = x * (y); 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 ▽ 7 / 6 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "7.285714", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "9 ▽ 7 / 6", "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小于y时,x ♡ y = y ** x * y + y; 其他情况下,x ♡ y = y + x - y * y + y。 和 ⊙,规则如下: 当x是偶数时,x ⊙ y = abs(x + y / x / y); 其他情况下,x ⊙ y = y - x ♡ x。 运算优先级:** = ♡ > * = / = % = ⊙ > + = -。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 8 ♡ 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 ♡ 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: 当y是5的倍数时,x ☆ y = 2 - y - x; 其他情况下,x ☆ y = x + x + y + x - y。 和 ♢,规则如下: 实数域上,x ♢ y = y * x + x * (x) + 5。 运算优先级:♢ > ** = ☆ > * = / = % > + = -。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 8 ♢ 1 ☆ 2 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "231", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "8 ♢ 1 ☆ 2", "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 = x + y - x * 5。 和 ⊙,规则如下: 当y是5的倍数时,x ⊙ y = y * x; 其他情况下,x ⊙ y = x - (x) - y。 运算优先级:◎ > ⊙ > ** > * = / = % > + = -。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 5 * 10 ⊙ 2 ◎ 10 ◎ 3 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "-250", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "5 * 10 ⊙ 2 ◎ 10 ◎ 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 = (y + x) - y + x. The precedence of operations: ** > * = / = % = △ > + = -。 Parentheses have the highest priority, and the expression inside the parentheses is calculated first. Please calculate the value of the expression: 7 Please fill your final ...
{ "game_data": { "answer": "7", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "7", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "nesting_depth": null...
logic-v2
Define ⊕, the rules are as follows: when y is odd, x ⊕ y = abs(y - x * x - y); otherwise, x ⊕ y = y + y * x * x. and ⊗, the rules are as follows: on the real number field, x ⊗ y = y + y / x. and ♡, the rules are as follows: when the sum of x and y is even, x ♡ y = y + x + (y) ** x; otherwise, x ♡ y = (x ⊗ y) ...
{ "game_data": { "answer": "89.857143", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "6 ♡ 9 ⊕ 7 ⊗ 3 / 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 * 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: 4 Please fill your fina...
{ "game_data": { "answer": "4", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "4", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "nesting_depth": null...