from __future__ import annotations

import math
from collections.abc import Callable






def        __UpperCAmelCase    (       UpperCAmelCase,		UpperCAmelCase,		UpperCAmelCase,		UpperCAmelCase = 100,		)->       float:



   """simple docstring"""







   lowercase							=		x_start
   lowercase							=		fnc(a_       )
   lowercase							=		0.0

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

      # Increment step
      lowercase							=		xa
      lowercase							=		fxa

   return length


if __name__ == "__main__":






      def        __UpperCAmelCase    (       UpperCAmelCase       )->       Dict:



         """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:")
      A_      =      10
      while i <= 100000:
            print(F"With {i} steps: {line_length(f, -10, 10, i)}")
            i *= 10






from __future__ import annotations

import math






def        __UpperCAmelCase    (       UpperCAmelCase       )->       list[int]:



			"""simple docstring"""







			if num <= 0:
						lowercase							=		f'{num}: Invalid input, please enter a positive integer.'
						raise ValueError(UpperCAmelCase       )

			lowercase							=		[True] * (num + 1)
			lowercase							=		[]
			lowercase							=		2
			lowercase							=		int(math.sqrt(UpperCAmelCase       )       )

			while start <= end:
						# If start is a prime
						if sieve[start] is True:
									prime.append(UpperCAmelCase       )

									# Set multiples of start be False
									for i in range(start * start,		num + 1,		UpperCAmelCase       ):
												if sieve[i] is True:
															lowercase							=		False

						start += 1

			for j in range(end + 1,		num + 1       ):
						if sieve[j] is True:
									prime.append(UpperCAmelCase       )

			return prime


if __name__ == "__main__":
						print(prime_sieve(int(input("Enter a positive integer: ").strip())))





