



import random







def 	lowerCamelCase_   (  _a    :		list					,						_a    :		Any  ):



    '''simple docstring'''




    UpperCAmelCase_						,      UpperCAmelCase_						,      UpperCAmelCase_			:    Dict   						= [], [], []
    for element in data:
        if element < pivot:
            less.append(SCREAMING_SNAKE_CASE_  )
        elif element > pivot:
            greater.append(SCREAMING_SNAKE_CASE_  )
        else:
            equal.append(SCREAMING_SNAKE_CASE_  )
    return less, equal, greater







def 	lowerCamelCase_   (  _a    :		list					,						_a    :		int  ):



    '''simple docstring'''




    if index >= len(SCREAMING_SNAKE_CASE_  ) or index < 0:
        return None

    UpperCAmelCase_			:    int   						= items[random.randint(0					,						len(SCREAMING_SNAKE_CASE_  ) - 1  )]
    UpperCAmelCase_			:    Any   						= 0
    UpperCAmelCase_						,      UpperCAmelCase_						,      UpperCAmelCase_			:    List[Any]   						= _partition(SCREAMING_SNAKE_CASE_					,						SCREAMING_SNAKE_CASE_  )
    UpperCAmelCase_			:    Optional[int]   						= len(SCREAMING_SNAKE_CASE_  )
    UpperCAmelCase_			:    Union[str, Any]   						= len(SCREAMING_SNAKE_CASE_  )

    # index is the pivot
    if m <= index < m + count:
        return pivot
    # must be in smaller
    elif m > index:
        return quick_select(SCREAMING_SNAKE_CASE_					,						SCREAMING_SNAKE_CASE_  )
    # must be in larger
    else:
        return quick_select(SCREAMING_SNAKE_CASE_					,						index - (m + count)  )




"""simple docstring"""




from __future__ import annotations

from collections.abc import Callable


def     lowercase			(SCREAMING_SNAKE_CASE_		:				Callable[[int | float], int | float] ,			SCREAMING_SNAKE_CASE_		:				int | float ,			SCREAMING_SNAKE_CASE_		:				int | float ,			SCREAMING_SNAKE_CASE_		:				int = 1_00 ,			)   ->						float:
						SCREAMING_SNAKE_CASE													=					x_start
						SCREAMING_SNAKE_CASE													=					fnc(SCREAMING_SNAKE_CASE_  )
						SCREAMING_SNAKE_CASE													=					0.0
						for _ in range(SCREAMING_SNAKE_CASE_  ):
												# Approximates small segments of curve as linear and solve
												# for trapezoidal area
												SCREAMING_SNAKE_CASE													=					(x_end - x_start) / steps + xa
												SCREAMING_SNAKE_CASE													=					fnc(SCREAMING_SNAKE_CASE_  )
												area += abs(fxa + fxa  ) * (xa - xa) / 2
												# Increment step
												SCREAMING_SNAKE_CASE													=					xa
												SCREAMING_SNAKE_CASE													=					fxa
						return area


if __name__ == "__main__":


	def     lowercase			(SCREAMING_SNAKE_CASE_		:				Optional[int]  )   ->						Dict:
							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:''')
	__UpperCamelCase						=      10
	while i <= 100000:
		print(f'''with {i} steps: {trapezoidal_area(f, -5, 5, i)}''')
		i *= 10


