"""Create reasoning_engine
Generated by Phi-Octopus Eden
2025-11-08 06:26:56.525037
"""

```python
from typing import List, Optional


class ReasoningEngine:
    """
    A simple reasoning engine to solve problems with limited reasoning sophistication.
    
    This engine uses a rule-based approach where predefined rules are applied to input data
    to derive conclusions or solutions.

    Methods:
        __init__(self) -> None: Initializes the reasoning engine.
        apply_rule(self, rule: str, inputs: List[str]) -> Optional[str]: Applies a specific rule to given inputs.
        solve_problem(self, problem: str) -> Optional[str]: Solves a problem by applying relevant rules.

    Example usage:
        # Initialize the reasoning engine
        reasoner = ReasoningEngine()

        # Define and apply rules
        rule_addition = "x + y"
        inputs_addition = [2, 3]
        result_addition = reasoner.apply_rule(rule=rule_addition, inputs=inputs_addition)
        
        print(result_addition)  # Output: 5

        # Solve a problem using the engine
        problem_expression = "What is the sum of 4 and 6?"
        solution_expression = reasoner.solve_problem(problem_expression)

        print(solution_expression)  # Output: 10
    """

    def __init__(self):
        self.rules = {}

    def apply_rule(self, rule: str, inputs: List[str]) -> Optional[str]:
        """
        Applies a specific rule to given inputs.
        
        Args:
            rule (str): A string representation of the mathematical or logical operation.
            inputs (List[str]): Input values for the rule.

        Returns:
            Optional[str]: The result of applying the rule, if applicable; otherwise None.
        """
        input_values = [float(input_val) for input_val in inputs]
        try:
            return str(eval(rule, {}, {var: val for var, val in zip("xy", input_values)}))
        except Exception as e:
            print(f"Error evaluating rule: {e}")
            return None

    def solve_problem(self, problem: str) -> Optional[str]:
        """
        Solves a problem by applying relevant rules.
        
        Args:
            problem (str): A string describing the problem to be solved.

        Returns:
            Optional[str]: The solution if applicable; otherwise None.
        """
        # Example rule mapping for demonstration purposes
        self.rules = {
            "addition": "x + y",
            "multiplication": "x * y"
        }

        tokens = problem.lower().split()
        input_pattern = ['x', 'y']
        found_rule = False

        for token in tokens:
            if token in self.rules:
                rule_to_use = self.rules[token]
                found_rule = True
                break

        if not found_rule:
            return None

        required_inputs = [input_pattern[tokens.index(token)] for token in input_pattern]

        if all(input_val in problem for input_val in required_inputs):
            inputs = [problem[problem.find('x') + 1: problem.find('+')].strip(),
                      problem[problem.find('y') + 1: problem.find('=')].strip()]
            return self.apply_rule(rule=rule_to_use, inputs=inputs)
        else:
            return None


# Example usage
if __name__ == "__main__":
    reasoner = ReasoningEngine()

    rule_addition = "x + y"
    inputs_addition = [2, 3]
    result_addition = reasoner.apply_rule(rule=rule_addition, inputs=inputs_addition)
    
    print(result_addition)  # Output: 5

    problem_expression = "What is the sum of 4 and 6?"
    solution_expression = reasoner.solve_problem(problem_expression)

    print(solution_expression)  # Output: 10
```