

"""simple docstring"""




from math import pi, sqrt, tan
def   lowerCAmelCase						(					__UpperCamelCase      ):
 '''simple docstring'''





 if side_length < 0:
  raise ValueError("""surface_area_cube() only accepts non-negative values"""      )
 return 6 * side_length**2
def   lowerCAmelCase						(					__UpperCamelCase							,    __UpperCamelCase							,    __UpperCamelCase      ):
 '''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						(					__UpperCamelCase      ):
 '''simple docstring'''





 if radius < 0:
  raise ValueError("""surface_area_sphere() only accepts non-negative values"""      )
 return 4 * pi * radius**2
def   lowerCAmelCase						(					__UpperCamelCase      ):
 '''simple docstring'''





 if radius < 0:
  raise ValueError("""surface_area_hemisphere() only accepts non-negative values"""      )
 return 3 * pi * radius**2
def   lowerCAmelCase						(					__UpperCamelCase							,    __UpperCamelCase      ):
 '''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						(					__UpperCamelCase							,    __UpperCamelCase							,    __UpperCamelCase      ):
 '''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__					:  Dict					   =					(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						(					__UpperCamelCase							,    __UpperCamelCase      ):
 '''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						(					__UpperCamelCase							,    __UpperCamelCase      ):
 '''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   lowerCAmelCase						(					__UpperCamelCase							,    __UpperCamelCase      ):
 '''simple docstring'''





 if length < 0 or width < 0:
  raise ValueError("""area_rectangle() only accepts non-negative values"""      )
 return length * width
def   lowerCAmelCase						(					__UpperCamelCase      ):
 '''simple docstring'''





 if side_length < 0:
  raise ValueError("""area_square() only accepts non-negative values"""      )
 return side_length**2
def   lowerCAmelCase						(					__UpperCamelCase							,    __UpperCamelCase      ):
 '''simple docstring'''





 if base < 0 or height < 0:
  raise ValueError("""area_triangle() only accepts non-negative values"""      )
 return (base * height) / 2
def   lowerCAmelCase						(					__UpperCamelCase							,    __UpperCamelCase							,    __UpperCamelCase      ):
 '''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__					:  Optional[Any]					   =					(sidea + sidea + sidea) / 2
 UpperCAmelCase__					:  int					   =					sqrt(
     semi_perimeter
     * (semi_perimeter - sidea)
     * (semi_perimeter - sidea)
     * (semi_perimeter - sidea)      )
 return area
def   lowerCAmelCase						(					__UpperCamelCase							,    __UpperCamelCase      ):
 '''simple docstring'''





 if base < 0 or height < 0:
  raise ValueError("""area_parallelogram() only accepts non-negative values"""      )
 return base * height
def   lowerCAmelCase						(					__UpperCamelCase							,    __UpperCamelCase							,    __UpperCamelCase      ):
 '''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						(					__UpperCamelCase      ):
 '''simple docstring'''





 if radius < 0:
  raise ValueError("""area_circle() only accepts non-negative values"""      )
 return pi * radius**2
def   lowerCAmelCase						(					__UpperCamelCase							,    __UpperCamelCase      ):
 '''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						(					__UpperCamelCase							,    __UpperCamelCase      ):
 '''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						(					__UpperCamelCase							,    __UpperCamelCase      ):
 '''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) = }")








"""simple docstring"""




def   lowerCAmelCase						(					__UpperCamelCase = 1000      ):
 '''simple docstring'''





 return sum(2 * a * ((a - 1) // 2) for a in range(3							,    n + 1      )      )


if __name__ == "__main__":
      print(solution())





