




'''simple docstring'''





from __future__ import annotations

import math
from collections.abc import Callable


def      UpperCamelCase_(	snake_case							:       Callable[[int | float], int | float]							,				snake_case							:       int | float							,				snake_case							:       int | float							,				snake_case							:       int = 1_0_0							,				):

							'''simple docstring'''






							snake_case_						=      x_start
							snake_case_						=      fnc(snake_case     )
							snake_case_						=      0.0

							for _ in range(snake_case     ):
														# Approximates curve as a sequence of linear lines and sums their length
														snake_case_						=      (x_end - x_start) / steps + xa
														snake_case_						=      fnc(snake_case     )
														length += math.hypot(xa - xa							,				fxa - fxa     )

														# Increment step
														snake_case_						=      xa
														snake_case_						=      fxa

							return length


if __name__ == "__main__":


		def      UpperCamelCase_(	snake_case							:       List[Any]     ):

									'''simple docstring'''






									return math.sin(1_0 * x     )

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










from __future__ import annotations







def SCREAMING_SNAKE_CASE				(       lowercase_ ,				lowercase_ ,				lowercase_						)   ->       tuple[float, list[float]]:



       """simple docstring"""

       A__       =    list(range(len(lowercase_						)						)						)
       A__       =    [v / w for v, w in zip(lowercase_ ,				lowercase_						)]
       index.sort(key=lambda lowercase_						: ratio[i] ,				reverse=lowercase_						)

       A__       =    0
       A__       =    [0] * len(lowercase_						)
       for i in index:
              if weight[i] <= capacity:
                     A__       =    1
                     max_value += value[i]
                     capacity -= weight[i]
              else:
                     A__       =    capacity / weight[i]
                     max_value += value[i] * capacity / weight[i]
                     break

       return max_value, fractions


if __name__ == "__main__":
  import doctest

  doctest.testmod()


