
"""simple docstring"""







from __future__ import annotations
def   __UpperCamelCase   (					SCREAMING_SNAKE_CASE							,    SCREAMING_SNAKE_CASE )  ->     list[int]:







       """simple docstring"""


       __snake_case     			=       0
       __snake_case     			=       len(SCREAMING_SNAKE_CASE ) - 1

       while i < j:
              if nums[i] + nums[j] == target:
                     return [i, j]
              elif nums[i] + nums[j] < target:
                     __snake_case     			=       i + 1
              else:
                     __snake_case     			=       j - 1

       return []


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  print(F"""{two_pointer([2, 7, 11, 15], 9) = }""")


"""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
