Part 1: Explain Higher-Order Functions (Conceptual):

Provide a clear definition of higher-order functions in Python. Explain the characteristics that make a function 'higher-order' and provide a simple, illustrative Python code example of a higher-order function.

Part 2: Implement @log Decorator (Practical):

Implement a Python decorator named @log. This decorator should, when applied to a function, perform the following actions:

• Before the decorated function executes, print a log message indicating the function's name and all the arguments it received (positional and keyword arguments).
• After the decorated function executes, print a log message indicating the function's name and its return value.
• The log messages should be descriptive and clearly formatted (e.g., 'Calling function_name with args (...) and kwargs {...}', 'function_name returned ...').

Part 3: Implement @timeit Decorator (Practical):

Implement a Python decorator named @timeit. This decorator should, when applied to a function, measure the total execution time of the decorated function. After the function completes, it should print the execution time to the console in a user-friendly format (e.g., 'Function 'function_name' executed in X.XXX seconds'). Ensure precision up to at least three decimal places.

Part 4: Demonstrate Usage (Application):

Create two distinct Python functions:

• calculate_factorial(n): A function that calculates the factorial of a given number n.
• simulate_work(seconds): A function that takes a number of seconds and simulates work by pausing execution for that duration (e.g., using time.sleep).

Apply both the @log and @timeit decorators to each of these functions. Then, show example calls for both decorated functions, demonstrating how the decorators' outputs are displayed.

Part 5: Discuss Benefits (Conceptual):

Explain the key advantages of using decorators for adding cross-cutting concerns like logging and timing, compared to manually adding the same boilerplate code within each function. Discuss concepts like code reusability, separation of concerns, and maintainability.