



from math import pi, sqrt, tan

def      lowerCAmelCase_					(  _lowercase    :       str)							->	Dict:







			"""simple docstring"""



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

def      lowerCAmelCase_					(  _lowercase    :       str						,       _lowercase    :       Optional[int]						,       _lowercase    :       Any)							->	int:







			"""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      lowerCAmelCase_					(  _lowercase    :       List[str])							->	Tuple:







			"""simple docstring"""



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

def      lowerCAmelCase_					(  _lowercase    :       List[str])							->	str:







			"""simple docstring"""



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

def      lowerCAmelCase_					(  _lowercase    :       Optional[Any]						,       _lowercase    :       Optional[int])							->	List[str]:







			"""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      lowerCAmelCase_					(  _lowercase    :       Tuple						,       _lowercase    :       List[Any]						,       _lowercase    :       List[str])							->	Optional[int]:







			"""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      lowerCAmelCase_					(  _lowercase    :       Optional[Any]						,       _lowercase    :       Optional[Any])							->	Dict:







			"""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      lowerCAmelCase_					(  _lowercase    :       List[str]						,       _lowercase    :       Dict)							->	int:







			"""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(a__						,       2) * torus_radius * tube_radius

def      lowerCAmelCase_					(  _lowercase    :       List[str]						,       _lowercase    :       Tuple)							->	List[Any]:







			"""simple docstring"""



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

def      lowerCAmelCase_					(  _lowercase    :       int)							->	int:







			"""simple docstring"""



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

def      lowerCAmelCase_					(  _lowercase    :       List[str]						,       _lowercase    :       List[Any])							->	int:







			"""simple docstring"""



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

def      lowerCAmelCase_					(  _lowercase    :       int						,       _lowercase    :       Any						,       _lowercase    :       str)							->	int:







			"""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__       :						int							=  (sidea + sidea + sidea) / 2
			a__       :						List[str]							=  sqrt(
			    semi_perimeter
			    * (semi_perimeter - sidea)
			    * (semi_perimeter - sidea)
			    * (semi_perimeter - sidea))
			return area

def      lowerCAmelCase_					(  _lowercase    :       str						,       _lowercase    :       List[str])							->	Union[str, Any]:







			"""simple docstring"""



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

def      lowerCAmelCase_					(  _lowercase    :       List[Any]						,       _lowercase    :       int						,       _lowercase    :       int)							->	Optional[Any]:







			"""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      lowerCAmelCase_					(  _lowercase    :       int)							->	str:







			"""simple docstring"""



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

def      lowerCAmelCase_					(  _lowercase    :       Tuple						,       _lowercase    :       Union[str, Any])							->	Union[str, Any]:







			"""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      lowerCAmelCase_					(  _lowercase    :       Tuple						,       _lowercase    :       Optional[Any])							->	Optional[int]:







			"""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      lowerCAmelCase_					(  _lowercase    :       str						,       _lowercase    :       Dict)							->	int:







			"""simple docstring"""



			if not isinstance(a__						,       a__) 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) = }')











_lowercase		:				Optional[int]      		=[
    (1000, "M"),
    (900, "CM"),
    (500, "D"),
    (400, "CD"),
    (100, "C"),
    (90, "XC"),
    (50, "L"),
    (40, "XL"),
    (10, "X"),
    (9, "IX"),
    (5, "V"),
    (4, "IV"),
    (1, "I"),
]

def      lowerCAmelCase_					(  _lowercase    :       str)							->	int:







			"""simple docstring"""
			a__       :						Union[str, Any]							=  {"""I""": 1, """V""": 5, """X""": 10, """L""": 50, """C""": 100, """D""": 500, """M""": 1000}
			a__       :						List[Any]							=  0
			a__       :						Dict							=  0
			while place < len(_lowercase):
						if (place + 1 < len(_lowercase)) and (vals[roman[place]] < vals[roman[place + 1]]):
									total += vals[roman[place + 1]] - vals[roman[place]]
									place += 2
						else:
									total += vals[roman[place]]
									place += 1
			return total

def      lowerCAmelCase_					(  _lowercase    :       int)							->	str:







			"""simple docstring"""
			a__       :						Optional[Any]							=  []
			for arabic, roman in ROMAN:
						((a__)	,						(a__))       :						Optional[Any]							=  divmod(_lowercase						,       _lowercase)
						result.append(roman * factor)
						if number == 0:
									break
			return "".join(_lowercase)


if __name__ == "__main__":
		import doctest

		doctest.testmod()




