"""simple docstring"""







import random



def 			lowercase__(       __SCREAMING_SNAKE_CASE							:     list     ,			__SCREAMING_SNAKE_CASE							:     Any      ):
     lowercase_							,  lowercase_							,  lowercase_	:				List[str]													=	[], [], []
     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 			lowercase__(       __SCREAMING_SNAKE_CASE							:     list     ,			__SCREAMING_SNAKE_CASE							:     int      ):
     # index = len(items) // 2 when trying to find the median
     #   (value of index when items is sorted)

     # invalid input
     if index >= len(__SCREAMING_SNAKE_CASE      ) or index < 0:
          return None

     lowercase_	:				Tuple													=	items[random.randint(0     ,			len(__SCREAMING_SNAKE_CASE      ) - 1      )]
     lowercase_	:				Union[str, Any]													=	0
     lowercase_							,  lowercase_							,  lowercase_	:				Optional[int]													=	_partition(__SCREAMING_SNAKE_CASE     ,			__SCREAMING_SNAKE_CASE      )
     lowercase_	:				int													=	len(__SCREAMING_SNAKE_CASE      )
     lowercase_	:				Optional[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

import math
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     ,			):
     lowercase_	:				Dict													=	x_start
     lowercase_	:				Optional[Any]													=	fnc(__SCREAMING_SNAKE_CASE      )
     lowercase_	:				Optional[Any]													=	0.0

     for _ in range(__SCREAMING_SNAKE_CASE      ):
          # Approximates curve as a sequence of linear lines and sums their length
          lowercase_	:				Union[str, Any]													=	(x_end - x_start) / steps + xa
          lowercase_	:				str													=	fnc(__SCREAMING_SNAKE_CASE      )
          length += math.hypot(xa - xa     ,			fxa - fxa      )

          # Increment step
          lowercase_	:				List[Any]													=	xa
          lowercase_	:				Optional[Any]													=	fxa

     return length


if __name__ == "__main__":



       def 			lowercase__(       __SCREAMING_SNAKE_CASE							:     Any      ):
            return math.sin(10 * x      )

       print("f(x) = sin(10 * x)")
       print("The length of the curve from x = -10 to x = 10 is:")
       __SCREAMING_SNAKE_CASE    	=10
       while i <= 10_0000:
              print(F"With {i} steps: {line_length(f, -10, 10, i)}")
              i *= 10

