"""simple docstring"""




from math import pi, sqrt, tan




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




		if side_length < 0:
				raise ValueError('surface_area_cube() only accepts non-negative values'     )
		return 6 * side_length**2




def     UpperCamelCase						(	__lowercase						:			float						,__lowercase						:			float						,__lowercase						:			float     ):
		'''simple docstring'''




		if length < 0 or breadth < 0 or height < 0:
				raise ValueError('surface_area_cuboid() only accepts non-negative values'     )
		return 2 * ((length * breadth) + (breadth * height) + (length * height))




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




		if radius < 0:
				raise ValueError('surface_area_sphere() only accepts non-negative values'     )
		return 4 * pi * radius**2




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




		if radius < 0:
				raise ValueError('surface_area_hemisphere() only accepts non-negative values'     )
		return 3 * pi * radius**2




def     UpperCamelCase						(	__lowercase						:			float						,__lowercase						:			float     ):
		'''simple docstring'''




		if radius < 0 or height < 0:
				raise ValueError('surface_area_cone() only accepts non-negative values'     )
		return pi * radius * (radius + (height**2 + radius**2) ** 0.5)




def     UpperCamelCase						(	__lowercase						:			float						,__lowercase						:			float						,__lowercase						:			float     ):
		'''simple docstring'''




		if radius_a < 0 or radius_a < 0 or height < 0:
				raise ValueError(
				    'surface_area_conical_frustum() only accepts non-negative values'     )
		A_		:    Optional[Any]         =				(height**2 + (radius_a - radius_a) ** 2) ** 0.5
		return pi * ((slant_height * (radius_a + radius_a)) + radius_a**2 + radius_a**2)




def     UpperCamelCase						(	__lowercase						:			float						,__lowercase						:			float     ):
		'''simple docstring'''




		if radius < 0 or height < 0:
				raise ValueError('surface_area_cylinder() only accepts non-negative values'     )
		return 2 * pi * radius * (height + radius)




def     UpperCamelCase						(	__lowercase						:			float						,__lowercase						:			float     ):
		'''simple docstring'''




		if torus_radius < 0 or tube_radius < 0:
				raise ValueError('surface_area_torus() only accepts non-negative values'     )
		if torus_radius < tube_radius:
				raise ValueError(
				    'surface_area_torus() does not support spindle or self intersecting tori'     )
		return 4 * pow(_UpperCamelCase						,2     ) * torus_radius * tube_radius




def     UpperCamelCase						(	__lowercase						:			float						,__lowercase						:			float     ):
		'''simple docstring'''




		if length < 0 or width < 0:
				raise ValueError('area_rectangle() only accepts non-negative values'     )
		return length * width




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




		if side_length < 0:
				raise ValueError('area_square() only accepts non-negative values'     )
		return side_length**2




def     UpperCamelCase						(	__lowercase						:			float						,__lowercase						:			float     ):
		'''simple docstring'''




		if base < 0 or height < 0:
				raise ValueError('area_triangle() only accepts non-negative values'     )
		return (base * height) / 2




def     UpperCamelCase						(	__lowercase						:			float						,__lowercase						:			float						,__lowercase						:			float     ):
		'''simple docstring'''




		if sidea < 0 or sidea < 0 or sidea < 0:
				raise ValueError('area_triangle_three_sides() only accepts non-negative values'     )
		elif sidea + sidea < sidea or sidea + sidea < sidea or sidea + sidea < sidea:
				raise ValueError('Given three sides do not form a triangle'     )
		A_		:    str         =				(sidea + sidea + sidea) / 2
		A_		:    Any         =				sqrt(
		    semi_perimeter
		    * (semi_perimeter - sidea)
		    * (semi_perimeter - sidea)
		    * (semi_perimeter - sidea)     )
		return area




def     UpperCamelCase						(	__lowercase						:			float						,__lowercase						:			float     ):
		'''simple docstring'''




		if base < 0 or height < 0:
				raise ValueError('area_parallelogram() only accepts non-negative values'     )
		return base * height




def     UpperCamelCase						(	__lowercase						:			float						,__lowercase						:			float						,__lowercase						:			float     ):
		'''simple docstring'''




		if basea < 0 or basea < 0 or height < 0:
				raise ValueError('area_trapezium() only accepts non-negative values'     )
		return 1 / 2 * (basea + basea) * height




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




		if radius < 0:
				raise ValueError('area_circle() only accepts non-negative values'     )
		return pi * radius**2




def     UpperCamelCase						(	__lowercase						:			float						,__lowercase						:			float     ):
		'''simple docstring'''




		if radius_x < 0 or radius_y < 0:
				raise ValueError('area_ellipse() only accepts non-negative values'     )
		return pi * radius_x * radius_y




def     UpperCamelCase						(	__lowercase						:			float						,__lowercase						:			float     ):
		'''simple docstring'''




		if diagonal_a < 0 or diagonal_a < 0:
				raise ValueError('area_rhombus() only accepts non-negative values'     )
		return 1 / 2 * diagonal_a * diagonal_a




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




		if not isinstance(_UpperCamelCase						,_UpperCamelCase     ) or sides < 3:
				raise ValueError(
				    'area_reg_polygon() only accepts integers greater than or \
equal to three as number of sides'     )
		elif length < 0:
				raise ValueError(
				    'area_reg_polygon() only accepts non-negative values as \
length of a side'     )
		return (sides * length**2) / (4 * tan(pi / sides     ))
		return (sides * length**2) / (4 * tan(pi / sides     ))


if __name__ == "__main__":
	import doctest

	doctest.testmod(verbose=True)  # verbose so we can see methods missing tests

	print("""[DEMO] Areas of various geometric shapes: \n""")
	print(F"""Rectangle: {area_rectangle(10, 20) = }""")
	print(F"""Square: {area_square(10) = }""")
	print(F"""Triangle: {area_triangle(10, 10) = }""")
	print(F"""Triangle: {area_triangle_three_sides(5, 12, 13) = }""")
	print(F"""Parallelogram: {area_parallelogram(10, 20) = }""")
	print(F"""Rhombus: {area_rhombus(10, 20) = }""")
	print(F"""Trapezium: {area_trapezium(10, 20, 30) = }""")
	print(F"""Circle: {area_circle(20) = }""")
	print(F"""Ellipse: {area_ellipse(10, 20) = }""")
	print("""\nSurface Areas of various geometric shapes: \n""")
	print(F"""Cube: {surface_area_cube(20) = }""")
	print(F"""Cuboid: {surface_area_cuboid(10, 20, 30) = }""")
	print(F"""Sphere: {surface_area_sphere(20) = }""")
	print(F"""Hemisphere: {surface_area_hemisphere(20) = }""")
	print(F"""Cone: {surface_area_cone(10, 20) = }""")
	print(F"""Conical Frustum: {surface_area_conical_frustum(10, 20, 30) = }""")
	print(F"""Cylinder: {surface_area_cylinder(10, 20) = }""")
	print(F"""Torus: {surface_area_torus(20, 10) = }""")
	print(F"""Equilateral Triangle: {area_reg_polygon(3, 10) = }""")
	print(F"""Square: {area_reg_polygon(4, 10) = }""")
	print(F"""Reqular Pentagon: {area_reg_polygon(5, 10) = }""")







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() = }""")






