
from math import pi, sqrt, tan




def 	_SCREAMING_SNAKE_CASE					(		_lowerCamelCase :			float)					->    float:






							'''simple docstring'''





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




def 	_SCREAMING_SNAKE_CASE					(		_lowerCamelCase :			float						,  _lowerCamelCase :			float						,  _lowerCamelCase :			float)					->    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 	_SCREAMING_SNAKE_CASE					(		_lowerCamelCase :			float)					->    float:






							'''simple docstring'''





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




def 	_SCREAMING_SNAKE_CASE					(		_lowerCamelCase :			float)					->    float:






							'''simple docstring'''





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




def 	_SCREAMING_SNAKE_CASE					(		_lowerCamelCase :			float						,  _lowerCamelCase :			float)					->    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 	_SCREAMING_SNAKE_CASE					(		_lowerCamelCase :			float						,  _lowerCamelCase :			float						,  _lowerCamelCase :			float)					->    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")
							__UpperCamelCase	:   Optional[int]			   =					(height**2 + (radius_a - radius_a) ** 2) ** 0.5
							return pi * ((slant_height * (radius_a + radius_a)) + radius_a**2 + radius_a**2)




def 	_SCREAMING_SNAKE_CASE					(		_lowerCamelCase :			float						,  _lowerCamelCase :			float)					->    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 	_SCREAMING_SNAKE_CASE					(		_lowerCamelCase :			float						,  _lowerCamelCase :			float)					->    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(_lowerCamelCase						,  2) * torus_radius * tube_radius




def 	_SCREAMING_SNAKE_CASE					(		_lowerCamelCase :			float						,  _lowerCamelCase :			float)					->    float:






							'''simple docstring'''





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




def 	_SCREAMING_SNAKE_CASE					(		_lowerCamelCase :			float)					->    float:






							'''simple docstring'''





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




def 	_SCREAMING_SNAKE_CASE					(		_lowerCamelCase :			float						,  _lowerCamelCase :			float)					->    float:






							'''simple docstring'''





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




def 	_SCREAMING_SNAKE_CASE					(		_lowerCamelCase :			float						,  _lowerCamelCase :			float						,  _lowerCamelCase :			float)					->    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")
							__UpperCamelCase	:   List[str]			   =					(sidea + sidea + sidea) / 2
							__UpperCamelCase	:   str			   =					sqrt(
							    semi_perimeter
							    * (semi_perimeter - sidea)
							    * (semi_perimeter - sidea)
							    * (semi_perimeter - sidea))
							return area




def 	_SCREAMING_SNAKE_CASE					(		_lowerCamelCase :			float						,  _lowerCamelCase :			float)					->    float:






							'''simple docstring'''





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




def 	_SCREAMING_SNAKE_CASE					(		_lowerCamelCase :			float						,  _lowerCamelCase :			float						,  _lowerCamelCase :			float)					->    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 	_SCREAMING_SNAKE_CASE					(		_lowerCamelCase :			float)					->    float:






							'''simple docstring'''





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




def 	_SCREAMING_SNAKE_CASE					(		_lowerCamelCase :			float						,  _lowerCamelCase :			float)					->    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 	_SCREAMING_SNAKE_CASE					(		_lowerCamelCase :			float						,  _lowerCamelCase :			float)					->    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 	_SCREAMING_SNAKE_CASE					(		_lowerCamelCase :			int						,  _lowerCamelCase :			float)					->    float:






							'''simple docstring'''





							if not isinstance(_lowerCamelCase						,  _lowerCamelCase) 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 __future__ import annotations

import math

lowercase  :					Any													=       '2020.9.26'
lowercase  :					Union[str, Any]													=       'xcodz-dot, cclaus, dhruvmanila'




def 	_SCREAMING_SNAKE_CASE					(		_lowerCamelCase :			float						,  _lowerCamelCase :			float						,  _lowerCamelCase :			float						,  _lowerCamelCase :			float						,  _lowerCamelCase :			float)					->    tuple[float, float]:






							'''simple docstring'''





							if not all(isinstance(_lowerCamelCase						,  (float, int)) for val in locals().values()):
														__UpperCamelCase	:   str			   =					F'Input values must either be float or int: {list(locals().values())}'
														raise TypeError(_lowerCamelCase)
							__UpperCamelCase	:   List[str]			   =					((x * distance) / (z + distance)) * scale
							__UpperCamelCase	:   List[Any]			   =					((y * distance) / (z + distance)) * scale
							return projected_x, projected_y




def 	_SCREAMING_SNAKE_CASE					(		_lowerCamelCase :			float						,  _lowerCamelCase :			float						,  _lowerCamelCase :			float						,  _lowerCamelCase :			str						,  _lowerCamelCase :			float)					->    tuple[float, float, float]:






							'''simple docstring'''





							if not isinstance(_lowerCamelCase						,  _lowerCamelCase):
														raise TypeError("Axis must be a str")
							__UpperCamelCase	:   str			   =					locals()
							del input_variables["axis"]
							if not all(isinstance(_lowerCamelCase						,  (float, int)) for val in input_variables.values()):
														__UpperCamelCase	:   Dict			   =					(
														    "Input values except axis must either be float or int: "
														    F'{list(input_variables.values())}'
														)
														raise TypeError(_lowerCamelCase)
							__UpperCamelCase	:   Optional[Any]			   =					(angle % 360) / 450 * 180 / math.pi
							if axis == "z":
														__UpperCamelCase	:   Tuple			   =					x * math.cos(_lowerCamelCase) - y * math.sin(_lowerCamelCase)
														__UpperCamelCase	:   Union[str, Any]			   =					y * math.cos(_lowerCamelCase) + x * math.sin(_lowerCamelCase)
														__UpperCamelCase	:   Any			   =					z
							elif axis == "x":
														__UpperCamelCase	:   Dict			   =					y * math.cos(_lowerCamelCase) - z * math.sin(_lowerCamelCase)
														__UpperCamelCase	:   Any			   =					z * math.cos(_lowerCamelCase) + y * math.sin(_lowerCamelCase)
														__UpperCamelCase	:   List[str]			   =					x
							elif axis == "y":
														__UpperCamelCase	:   Any			   =					x * math.cos(_lowerCamelCase) - z * math.sin(_lowerCamelCase)
														__UpperCamelCase	:   Any			   =					z * math.cos(_lowerCamelCase) + x * math.sin(_lowerCamelCase)
														__UpperCamelCase	:   Dict			   =					y
							else:
														raise ValueError("not a valid axis, choose one of 'x', 'y', 'z'")

							return new_x, new_y, new_z


if __name__ == "__main__":
		import doctest

		doctest.testmod()
		print(f"{convert_to_ad(1.0, 2.0, 3.0, 1_0.0, 1_0.0) = }")
		print(f"{rotate(1.0, 2.0, 3.0, 'y', 9_0.0) = }")