


'''simple docstring'''


from math import pi, sqrt, tan




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




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




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




def      lowerCamelCase					(      lowerCamelCase  :      float							,						lowerCamelCase  :      float):
      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					(      lowerCamelCase  :      float							,						lowerCamelCase  :      float							,						lowerCamelCase  :      float):
      if radius_a < 0 or radius_a < 0 or height < 0:
            raise ValueError(
                """surface_area_conical_frustum() only accepts non-negative values""")
      A_						:  List[str]          =				(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					(      lowerCamelCase  :      float							,						lowerCamelCase  :      float):
      if radius < 0 or height < 0:
            raise ValueError("""surface_area_cylinder() only accepts non-negative values""")
      return 2 * pi * radius * (height + radius)




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




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




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




def      lowerCamelCase					(      lowerCamelCase  :      float							,						lowerCamelCase  :      float							,						lowerCamelCase  :      float):
      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_						:  List[str]          =				(sidea + sidea + sidea) / 2
      A_						:  Optional[int]          =				sqrt(
          semi_perimeter
          * (semi_perimeter - sidea)
          * (semi_perimeter - sidea)
          * (semi_perimeter - sidea))
      return area




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




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




def      lowerCamelCase					(      lowerCamelCase  :      float							,						lowerCamelCase  :      float):
      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					(      lowerCamelCase  :      float							,						lowerCamelCase  :      float):
      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					(      lowerCamelCase  :      int							,						lowerCamelCase  :      float):
      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) = }""")




'''simple docstring'''


from sympy import diff, lambdify, symbols
from sympy.functions import *  # noqa: F403




def      lowerCamelCase					(      lowerCamelCase  :      str							,						lowerCamelCase  :      complex							,						lowerCamelCase  :      str = "x"							,						lowerCamelCase  :      float = 10**-10							,						lowerCamelCase  :      int = 1							,						):
      A_						:  int          =				symbols(lowerCamelCase)
      A_						:  List[Any]          =				lambdify(lowerCamelCase							,						lowerCamelCase)
      A_						:  List[str]          =				lambdify(lowerCamelCase							,						diff(lowerCamelCase							,						lowerCamelCase))

      A_						:  str          =				starting_point

      while True:
            if diff_function(lowerCamelCase) != 0:
                  A_						:  int          =				prev_guess - multiplicity * func(lowerCamelCase) / diff_function(
                      lowerCamelCase)
            else:
                  raise ZeroDivisionError("""Could not find root""") from None

            # Precision is checked by comparing the difference of consecutive guesses
            if abs(next_guess - prev_guess) < precision:
                  return next_guess

            A_						:  Union[str, Any]          =				next_guess


# Let's Execute
if __name__ == "__main__":
     # Find root of trigonometric function
     # Find value of pi
     print(f"""The root of sin(x) = 0 is {newton_raphson('sin(x)', 2)}""")

     # Find root of polynomial
     # Find fourth Root of 5
     print(f"""The root of x**4 - 5 = 0 is {newton_raphson('x**4 -5', 0.4 +5j)}""")

     # Find value of e
     print(
         'The root of log(y) - 1 = 0 is ',
         f"""{newton_raphson('log(y) - 1', 2, variable='y')}""",
     )

     # Exponential Roots
     print(
         'The root of exp(x) - 1 = 0 is',
         f"""{newton_raphson('exp(x) - 1', 10, precision=0.0_0_5)}""",
     )

     # Find root of cos(x)
     print(f"""The root of cos(x) = 0 is {newton_raphson('cos(x)', 0)}""")
