





"""simple docstring"""



from __future__ import annotations

from collections.abc import Callable







def 	__lowercase  (     snake_case_						:						Callable[[int | float], int | float]       ,snake_case_						:						int | float       ,snake_case_						:						int | float       ,snake_case_						:						int = 100       ,)     ->float:



    '''simple docstring'''







    __A					:		Tuple						=  x_start
    __A					:		List[str]						=  fnc(snake_case_		)
    __A					:		int						=  0.0

    for _ in range(snake_case_		):
        # Approximates small segments of curve as linear and solve
        # for trapezoidal area
        __A					:		List[str]						=  (x_end - x_start) / steps + xa
        __A					:		Optional[Any]						=  fnc(snake_case_		)
        area += abs(fxa + fxa		) * (xa - xa) / 2

        # Increment step
        __A					:		Dict						=  xa
        __A					:		Optional[Any]						=  fxa
    return area


if __name__ == "__main__":







       def 	__lowercase  (     snake_case_						:						List[Any]		)     ->Union[str, Any]:



           '''simple docstring'''







           return x**3

       print("""f(x) = x^3""")
       print("""The area between the curve, x = -10, x = 10 and the x axis is:""")
       a_				=    10
       while i <= 100000:
              a_				=    trapezoidal_area(f, -5, 5, i)
              print(f'''with {i} steps: {area}''')
              i *= 10











"""simple docstring"""



def 	__lowercase  (     snake_case_						:						Union[str, Any]		)     ->Optional[int]:



    '''simple docstring'''







    __A					:		Dict						=  [701, 301, 132, 57, 23, 10, 4, 1]
    for gap in gaps:
        for i in range(snake_case_       ,len(snake_case_		)		):
            __A					:		Tuple						=  collection[i]
            __A					:		Union[str, Any]						=  i
            while j >= gap and collection[j - gap] > insert_value:
                __A					:		Optional[int]						=  collection[j - gap]
                j -= gap
            if j != i:
                __A					:		Optional[int]						=  insert_value
    return collection


if __name__ == "__main__":
       from doctest import testmod

       testmod()
       a_				=    input("""Enter numbers separated by a comma:\n""").strip()
       a_				=    [int(item) for item in user_input.split(""",""")]
       print(shell_sort(unsorted))




