





from __future__ import annotations



def A_     (		A__		,				A__ = None		,				A__ = None    )  ->		None:


       if start is None:
              a__						:     Optional[Any]			=    0

       if end is None:
              a__						:     int			=    len(_lowerCamelCase    ) - 1

       if start >= end:
              return

       a__						:     str			=    (start + end) // 2

       slowsort(_lowerCamelCase		,				_lowerCamelCase		,				_lowerCamelCase    )
       slowsort(_lowerCamelCase		,				mid + 1		,				_lowerCamelCase    )

       if sequence[end] < sequence[mid]:
              a__						:     List[str]			=    sequence[mid], sequence[end]

       slowsort(_lowerCamelCase		,				_lowerCamelCase		,				end - 1    )


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

    testmod()









from __future__ import annotations

from collections.abc import Callable



def A_     (		A__		,				A__		,				A__		,				A__ = 100		,				)  ->		float:
       a__						:     Dict			=    x_start
       a__						:     Any			=    fnc(A__    )
       a__						:     Optional[int]			=    0.0
       for _ in range(A__    ):
              # Approximates small segments of curve as linear and solve
              # for trapezoidal area
              a__						:     Union[str, Any]			=    (x_end - x_start) / steps + xa
              a__						:     str			=    fnc(A__    )
              area += abs(fxa + fxa    ) * (xa - xa) / 2
              # Increment step
              a__						:     Optional[Any]			=    xa
              a__						:     Optional[int]			=    fxa
       return area


if __name__ == "__main__":



    def A_     (		A__    )  ->		List[str]:
           return x**3 + x**2

    print("""f(x) = x^3 + x^2""")
    print("""The area between the curve, x = -5, x = 5 and the x axis is:""")
    lowercase				:	Union[str, Any]      						=  1_0
    while i <= 1_0_0_0_0_0:
        print(F"""with {i} steps: {trapezoidal_area(f, -5, 5, i)}""")
        i *= 1_0


