

from __future__ import annotations

def        lowerCamelCase__       (    _a							,	_a):
	# Checks if the entire collection has been sorted
	if len(_a) <= 1 or n <= 1:
		return

	insert_next(_a							,	n - 1)
	rec_insertion_sort(_a							,	n - 1)

def        lowerCamelCase__       (    _a							,	_a):
	# Checks order between adjacent elements
	if index >= len(_a) or collection[index - 1] <= collection[index]:
		return

	# Swaps adjacent elements since they are not in ascending order
	SCREAMING_SNAKE_CASE   ,SCREAMING_SNAKE_CASE      :					List[Any]    =				(
	    collection[index],
	    collection[index - 1],
	)

	insert_next(_a							,	index + 1)


if __name__ == "__main__":
			a_     =			input('Enter integers separated by spaces: ')
			a_     =			[int(num) for num in numbers.split()]
			rec_insertion_sort(number_list, len(number_list))
			print(number_list)
"""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

