
'''simple docstring'''





def   A			(							A_				:       list     ,				A_				:       int     ,				A_				:       int							):
						if right <= left:
												return
						snake_case							:  str			=     left
						snake_case							:  Tuple			=     right
						snake_case							:  Optional[Any]			=     sorting[left]
						while i <= b:
												if sorting[i] < pivot:
																		snake_case,       snake_case							:  Optional[Any]			=     sorting[i], sorting[a]
																		a += 1
																		i += 1
												elif sorting[i] > pivot:
																		snake_case,       snake_case							:  Optional[Any]			=     sorting[i], sorting[b]
																		b -= 1
												else:
																		i += 1
						quick_sort_apartition(A_     ,				A_     ,				a - 1							)
						quick_sort_apartition(A_     ,				b + 1     ,				A_							)

def   A			(							A_				:       list     ,				A_				:       int     ,				A_				:       int							):
						if left < right:
												snake_case							:  List[Any]			=     lomuto_partition(A_     ,				A_     ,				A_							)
												quick_sort_lomuto_partition(A_     ,				A_     ,				pivot_index - 1							)
												quick_sort_lomuto_partition(A_     ,				pivot_index + 1     ,				A_							)

def   A			(							A_				:       list     ,				A_				:       int     ,				A_				:       int							):
						snake_case							:  str			=     sorting[right]
						snake_case							:  int			=     left
						for i in range(A_     ,				A_							):
												if sorting[i] < pivot:
																		snake_case,       snake_case							:  List[Any]			=     sorting[i], sorting[store_index]
																		store_index += 1
						snake_case,       snake_case							:  Union[str, Any]			=     sorting[store_index], sorting[right]
						return store_index

def   A			(							A_				:       list							):
						if len(A_							) <= 1:
												return sorting
						return (
						    three_way_radix_quicksort([i for i in sorting if i < sorting[0]]							)
						    + [i for i in sorting if i == sorting[0]]
						    + three_way_radix_quicksort([i for i in sorting if i > sorting[0]]							)
						)


if __name__ == "__main__":
						import doctest

						doctest.testmod(verbose=True)

						UpperCAmelCase            = input("Enter numbers separated by a comma:\n").strip()
						UpperCAmelCase            = [int(item) for item in user_input.split(",")]
						quick_sort_apartition(unsorted, 0, len(unsorted) - 1)
						print(unsorted)




'''simple docstring'''

from __future__ import annotations

from collections.abc import Callable




def  UpperCamelCase(	UpperCAmelCase_    ,			UpperCAmelCase_    ,			UpperCAmelCase_    ,			UpperCAmelCase_ = 1_00    ,			):
 UpperCAmelCase			:      Any		   =					x_start
 UpperCAmelCase			:      int		   =					fnc(UpperCAmelCase_      )
 UpperCAmelCase			:      str		   =					0.0

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

  # Increment step
  UpperCAmelCase			:      List[str]		   =					xa
  UpperCAmelCase			:      List[Any]		   =					fxa
 return area


if __name__ == "__main__":




 def  UpperCamelCase(	UpperCAmelCase_      ):
  return x**3

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




