
"""simple docstring"""







def   __UpperCamelCase   (					SCREAMING_SNAKE_CASE = 1							,    SCREAMING_SNAKE_CASE = 10_00 )  ->     int:







       """simple docstring"""


       __snake_case     			=       1
       __snake_case     			=       0

       for divide_by_number in range(SCREAMING_SNAKE_CASE							,    digit + 1 ):
              __snake_case     			=       []
              __snake_case     			=       numerator
              for _ in range(1							,    digit + 1 ):
                     if now_divide in has_been_divided:
                            if longest_list_length < len(SCREAMING_SNAKE_CASE ):
                                   __snake_case     			=       len(SCREAMING_SNAKE_CASE )
                                   __snake_case     			=       divide_by_number
                     else:
                            has_been_divided.append(SCREAMING_SNAKE_CASE )
                            __snake_case     			=       now_divide * 10 % divide_by_number

       return the_digit


# Tests
if __name__ == "__main__":
  import doctest

  doctest.testmod()


"""simple docstring"""







from __future__ import annotations

from collections.abc import Callable
def   __UpperCamelCase   (					SCREAMING_SNAKE_CASE							,    SCREAMING_SNAKE_CASE							,    SCREAMING_SNAKE_CASE							,    SCREAMING_SNAKE_CASE = 1_00							,    )  ->     float:







							"""simple docstring"""


							__snake_case     			=       x_start
							__snake_case     			=       fnc(SCREAMING_SNAKE_CASE )
							__snake_case     			=       0.0
							for _ in range(SCREAMING_SNAKE_CASE ):
														# Approximates small segments of curve as linear and solve
														# for trapezoidal area
														__snake_case     			=       (x_end - x_start) / steps + xa
														__snake_case     			=       fnc(SCREAMING_SNAKE_CASE )
														area += abs(fxa + fxa ) * (xa - xa) / 2
														# Increment step
														__snake_case     			=       xa
														__snake_case     			=       fxa
							return area


if __name__ == "__main__":
		def   __UpperCamelCase   (					SCREAMING_SNAKE_CASE )  ->     List[Any]:







									"""simple docstring"""


									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:""")
		_SCREAMING_SNAKE_CASE	       =      10
		while i <= 100_000:
				print(F"""with {i} steps: {trapezoidal_area(f, -5, 5, i)}""")
				i *= 10
