"""Create fallback_executor
Generated by Phi-Octopus Eden
2025-11-08 18:42:52.803018
"""

```python
class FallbackExecutor:
    """
    A class for executing tasks with limited error recovery capabilities.
    
    Attributes:
        fallback_func (Callable): The function to execute as a fallback in case of failure.
        max_attempts (int): Maximum number of attempts before giving up.

    Methods:
        run_task: Execute the task or fall back on a provided function if necessary.
    """
    
    def __init__(self, fallback_func: Callable[[Any], Any], max_attempts: int = 3):
        self.fallback_func = fallback_func
        self.max_attempts = max_attempts

    def run_task(self, task_func: Callable[[Any], Any], *args, **kwargs) -> Any:
        """
        Execute the given task function with error recovery.

        Args:
            task_func (Callable): The main task function to attempt.
            args: Positional arguments for the task function.
            kwargs: Keyword arguments for the task function.

        Returns:
            Any: The result of the successful execution or fallback function if all attempts fail.

        Raises:
            Exception: If all attempts at executing the task function fail and a fallback is not provided.
        """
        attempt = 0
        while attempt < self.max_attempts:
            try:
                return task_func(*args, **kwargs)
            except Exception as e:
                print(f"Attempt {attempt + 1} failed with error: {e}")
                if self.fallback_func:
                    return self.fallback_func(*args, **kwargs)
                else:
                    attempt += 1
        raise Exception("Failed to execute task and no fallback function provided")

# Example usage

def main_task(a: int, b: int) -> str:
    """Example main task that might fail."""
    if a > b:
        return f"Task succeeded with {a} > {b}"
    else:
        raise ValueError("Incorrect input for the task to succeed.")

fallback_func = lambda x, y: f"Fallback function executed with inputs: {x}, {y}"

executor = FallbackExecutor(fallback_func=fallback_func)
result = executor.run_task(main_task, 5, 10)  # Should work
print(result)

result = executor.run_task(main_task, 2, 3)  # Should fail and fallback
print(result)
```