


from __future__ import annotations

import math
from collections.abc import Callable


def 				lowerCamelCase__	(      a	:   Callable[[int | float], int | float]	,  a	:   int | float	,  a	:   int | float	,  a	:   int = 100	,  )    ->	float:





			"""simple docstring"""
			a__ :Optional[int]						  =    x_start
			a__ :Optional[int]						  =    fnc(a				)
			a__ :Union[str, Any]						  =    0.0

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

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

			return length


if __name__ == "__main__":


							def 				lowerCamelCase__	(      a	:   int				)    ->	Optional[Any]:





										"""simple docstring"""
										return math.sin(10 * x				)

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






def 				lowerCamelCase__	(      a	:   int = 1_000_000				)    ->	int:





			"""simple docstring"""
			a__ :int						  =    [i - 1 for i in range(limit + 1				)]

			for i in range(2	,  limit + 1				):
						if phi[i] == i - 1:
									for j in range(2 * i	,  limit + 1	,  a				):
												phi[j] -= phi[j] // i

			return sum(phi[2 : limit + 1]				)


if __name__ == "__main__":
		print(solution())


