"""simple docstring"""




from __future__ import annotations

from numpy import array, cos, cross, floataa, radians, sin
from numpy.typing import NDArray




def     UpperCamelCase						(	__lowercase						:			float						,__lowercase						:			float						,__lowercase						:			bool = False     ):
		'''simple docstring'''




		if radian_mode:
				return [magnitude * cos(__lowercase     ), magnitude * sin(__lowercase     )]
		return [magnitude * cos(radians(__lowercase     )     ), magnitude * sin(radians(__lowercase     )     )]




def     UpperCamelCase						(	__lowercase						:			NDArray[floataa]						,__lowercase						:			NDArray[floataa]						,__lowercase						:			float = 10**-1     ):
		'''simple docstring'''




		A_		:    NDArray[floataa]         =				cross(__lowercase						,__lowercase     )
		A_		:    float         =				sum(__lowercase     )
		return abs(__lowercase     ) < eps


if __name__ == "__main__":
	# Test to check if it works
	_UpperCAmelCase            =		array(
	    [
	        polar_force(718.4, 180 - 30),
	        polar_force(879.54, 45),
	        polar_force(100, -90),
	    ]
	)

	_UpperCAmelCase            =		array([[0, 0], [0, 0], [0, 0]])

	assert in_static_equilibrium(forces, location)

	# Problem 1 in image_data/2D_problems.jpg
	_UpperCAmelCase            =		array(
	    [
	        polar_force(30 * 9.81, 15),
	        polar_force(215, 180 - 45),
	        polar_force(264, 90 - 30),
	    ]
	)

	_UpperCAmelCase            =		array([[0, 0], [0, 0], [0, 0]])

	assert in_static_equilibrium(forces, location)

	# Problem in image_data/2D_problems_1.jpg
	_UpperCAmelCase            =		array([[0, -2000], [0, -1200], [0, 15600], [0, -12400]])

	_UpperCAmelCase            =		array([[0, 0], [6, 0], [10, 0], [12, 0]])

	assert in_static_equilibrium(forces, location)

	import doctest

	doctest.testmod()







from math import isqrt




def     UpperCamelCase						(	__lowercase						:			int     ):
		'''simple docstring'''




		return all(number % divisor != 0 for divisor in range(2						,isqrt(__lowercase     ) + 1     )     )




def     UpperCamelCase						(	__lowercase						:			int = 10**6     ):
		'''simple docstring'''




		A_		:    Optional[Any]         =				0
		A_		:    List[str]         =				1
		A_		:    Dict         =				7
		while prime_candidate < max_prime:
				primes_count += is_prime(__lowercase     )

				cube_index += 1
				prime_candidate += 6 * cube_index

		return primes_count


if __name__ == "__main__":
	print(F"""{solution() = }""")






