




'''simple docstring'''





from __future__ import annotations

from typing import Any

class        _a    (						__lowerCAmelCase							):
     pass







class        _a    :






     def __init__(			self ,_SCREAMING_SNAKE_CASE   )							->      None:
          _snake_case							=				data
          _snake_case							=				None






     def __iter__(			self   )							->      Any:
          _snake_case							=				self
          _snake_case							=				[]
          while node:
               if node in visited:
                    raise ContainsLoopError
               visited.append(_SCREAMING_SNAKE_CASE   )
               yield node.data
               _snake_case							=				node.next_node






     @property
     def     _lowercase     (			self   )							->      bool:
          try:
               list(self   )
               return False
          except ContainsLoopError:
               return True


if __name__ == "__main__":
   UpperCamelCase_						:      Dict       =						Node(1)
   UpperCamelCase_						:      List[str]       =						Node(2)
   UpperCamelCase_						:      Optional[Any]       =						Node(3)
   UpperCamelCase_						:      Optional[int]       =						Node(4)
   print(root_node.has_loop)  # False
   UpperCamelCase_						:      Tuple       =						root_node.next_node
   print(root_node.has_loop)  # True

   UpperCamelCase_						:      str       =						Node(5)
   UpperCamelCase_						:      Optional[Any]       =						Node(6)
   UpperCamelCase_						:      str       =						Node(5)
   UpperCamelCase_						:      Optional[int]       =						Node(6)
   print(root_node.has_loop)  # False

   UpperCamelCase_						:      Dict       =						Node(1)
   print(root_node.has_loop)  # False








'''simple docstring'''





from __future__ import annotations

from collections.abc import Callable





def      __a     (       _UpperCamelCase:   Callable[[int | float], int | float] ,						_UpperCamelCase:   int | float ,						_UpperCamelCase:   int | float ,						_UpperCamelCase:   int = 100 ,						)						->			float:

     """simple docstring"""




     _snake_case							=				x_start
     _snake_case							=				fnc(_UpperCamelCase   )
     _snake_case							=				0.0
     for _ in range(_UpperCamelCase   ):
          # Approximates small segments of curve as linear and solve
          # for trapezoidal area
          _snake_case							=				(x_end - x_start) / steps + xa
          _snake_case							=				fnc(_UpperCamelCase   )
          area += abs(fxa + fxa   ) * (xa - xa) / 2
          # Increment step
          _snake_case							=				xa
          _snake_case							=				fxa
     return area


if __name__ == "__main__":





   def      __a     (       _UpperCamelCase:   Any   )						->			Optional[int]:

        """simple docstring"""




        return x**3 + x**2

   print('''f(x) = x^3 + x^2''')
   print('''The area between the curve, x = -5, x = 5 and the x axis is:''')
   UpperCamelCase_						:      Optional[int]       =						10
   while i <= 100000:
      print(F'with {i} steps: {trapezoidal_area(f, -5, 5, i)}')
      i *= 10


