





'''simple docstring'''




from math import pi, sqrt, tan






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






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






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






def 	_lowerCAmelCase      (  __snake_case  :			float			,							__snake_case  :			float      )					->					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      (  __snake_case  :			float			,							__snake_case  :			float			,							__snake_case  :			float      )					->					float:
     if radius_a < 0 or radius_a < 0 or height < 0:
          raise ValueError(
              'surface_area_conical_frustum() only accepts non-negative values'      )
     __A						:			Union[str, 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      (  __snake_case  :			float			,							__snake_case  :			float      )					->					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      (  __snake_case  :			float			,							__snake_case  :			float      )					->					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(__snake_case			,							2      ) * torus_radius * tube_radius






def 	_lowerCAmelCase      (  __snake_case  :			float			,							__snake_case  :			float      )					->					float:
     if length < 0 or width < 0:
          raise ValueError('area_rectangle() only accepts non-negative values'      )
     return length * width






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






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






def 	_lowerCAmelCase      (  __snake_case  :			float			,							__snake_case  :			float			,							__snake_case  :			float      )					->					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						:			int								=	(sidea + sidea + sidea) / 2
     __A						:			Tuple								=	sqrt(
         semi_perimeter
         * (semi_perimeter - sidea)
         * (semi_perimeter - sidea)
         * (semi_perimeter - sidea)      )
     return area






def 	_lowerCAmelCase      (  __snake_case  :			float			,							__snake_case  :			float      )					->					float:
     if base < 0 or height < 0:
          raise ValueError('area_parallelogram() only accepts non-negative values'      )
     return base * height






def 	_lowerCAmelCase      (  __snake_case  :			float			,							__snake_case  :			float			,							__snake_case  :			float      )					->					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      (  __snake_case  :			float      )					->					float:
     if radius < 0:
          raise ValueError('area_circle() only accepts non-negative values'      )
     return pi * radius**2






def 	_lowerCAmelCase      (  __snake_case  :			float			,							__snake_case  :			float      )					->					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      (  __snake_case  :			float			,							__snake_case  :			float      )					->					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      (  __snake_case  :			int			,							__snake_case  :			float      )					->					float:
     if not isinstance(__snake_case			,							__snake_case      ) 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      (  __snake_case  :			str			,							__snake_case  :			str      )					->					float:

     def get_matched_characters(__snake_case  :			str			,							__snake_case  :			str      ) -> str:
          __A						:			Optional[int]								=	[]
          __A						:			Optional[Any]								=	min(len(_stra      )			,							len(_stra      )      ) // 2
          for i, l in enumerate(_stra      ):
               __A						:			str								=	int(max(0			,							i - limit      )      )
               __A						:			str								=	int(min(i + limit + 1			,							len(_stra      )      )      )
               if l in _stra[left:right]:
                    matched.append(__snake_case      )
                    __A						:			Dict								=	f'{_stra[0:_stra.index(__snake_case      )]} {_stra[_stra.index(__snake_case      ) + 1:]}'

          return "".join(__snake_case      )

     # matching characters
     __A						:			Any								=	get_matched_characters(__snake_case			,							__snake_case      )
     __A						:			str								=	get_matched_characters(__snake_case			,							__snake_case      )
     __A						:			str								=	len(__snake_case      )

     # transposition
     __A						:			Tuple								=	(
         len([(ca, ca) for ca, ca in zip(__snake_case			,							__snake_case      ) if ca != ca]      ) // 2
     )

     if not match_count:
          __A						:			int								=	0.0
     else:
          __A						:			Union[str, Any]								=	(
              1
              / 3
              * (
                  match_count / len(__snake_case      )
                  + match_count / len(__snake_case      )
                  + (match_count - transpositions) / match_count
              )
          )

     # common prefix up to 4 characters
     __A						:			Tuple								=	0
     for ca, ca in zip(stra[:4]			,							stra[:4]      ):
          if ca == ca:
               prefix_len += 1
          else:
               break

     return jaro + 0.1 * prefix_len * (1 - jaro)


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  print(jaro_winkler('''hello''', '''world'''))