


'''simple docstring'''
from __future__ import annotations

import math
from collections.abc import Callable




def 	_A  (       A							,A							,A							,A = 1_0_0							,)  ->				float:
	lowercase						:		List[Any]   					=		x_start
	lowercase						:		Any   					=		fnc(A							)
	lowercase						:		Dict   					=		0.0

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

		# Increment step
		lowercase						:		Optional[int]   					=		xa
		lowercase						:		Any   					=		fxa

	return length


if __name__ == "__main__":




					def 	_A  (       A							)  ->				Optional[Any]:
						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:""")
					lowerCAmelCase   : List[Any]             =				1_0
					while i <= 1_0_0_0_0_0:
										print(F'''With {i} steps: {line_length(f, -1_0, 1_0, i)}''')
										i *= 1_0






'''simple docstring'''
def 	_A  (       A							)  ->				list:
	lowercase						:		str   					=		int(A							)
	if n_element < 1:
		lowercase						:		List[Any]   					=		ValueError("a should be a positive number"							)
		raise my_error

	lowercase						:		List[Any]   					=		[1]
	lowercase					,		lowercase					,		lowercase						:		Tuple   					=		(0, 0, 0)
	lowercase						:		Dict   					=		1
	while index < n_element:
		while hamming_list[i] * 2 <= hamming_list[-1]:
			i += 1
		while hamming_list[j] * 3 <= hamming_list[-1]:
			j += 1
		while hamming_list[k] * 5 <= hamming_list[-1]:
			k += 1
		hamming_list.append(
		    min(hamming_list[i] * 2							,hamming_list[j] * 3							,hamming_list[k] * 5							)							)
		index += 1
	return hamming_list


if __name__ == "__main__":
					lowerCAmelCase   : Union[str, Any]             =				input("""Enter the last number (nth term) of the Hamming Number Series: """)
					print("""Formula of Hamming Number Series => 2^i * 3^j * 5^k""")
					lowerCAmelCase   : Tuple             =				hamming(int(n))
					print("""-----------------------------------------------------""")
					print(F'''The list with nth numbers is: {hamming_numbers}''')
					print("""-----------------------------------------------------""")


