





class 			A__   :




   """simple docstring"""



   def __init__( self)      ->						Optional[Any]:







          '''simple docstring'''

          a__						:     Any			=    {}

   def 							__lowercase		( self)      ->						None:







          '''simple docstring'''

          print(self.vertex)
          for i in self.vertex:
                 print(lowercase ,  ' -> ' ,  ' -> '.join([str(lowercase) for j in self.vertex[i]]))

   def 							__lowercase		( self ,  lowercase ,  lowercase)      ->						None:







          '''simple docstring'''

          if from_vertex in self.vertex:
                 self.vertex[from_vertex].append(lowercase)
          else:
                 # else make a new vertex
                 a__						:     str			=    [to_vertex]

   def 							__lowercase		( self)      ->						None:







          '''simple docstring'''

          a__						:     Tuple			=    [False] * len(self.vertex)

          # call the recursive helper function
          for i in range(len(self.vertex)):
                 if not visited[i]:
                        self.dfs_recursive(lowercase ,  lowercase)

   def 							__lowercase		( self ,  lowercase ,  lowercase)      ->						None:







          '''simple docstring'''

          a__						:     Optional[int]			=    True

          print(lowercase ,  end=' ')

          # Recur for all the vertices that are adjacent to this node
          for i in self.vertex:
                 if not visited[i]:
                        self.dfs_recursive(lowercase ,  lowercase)


if __name__ == "__main__":
    lowercase				:	Dict      						=  Graph()
    g.add_edge(0, 1)
    g.add_edge(0, 2)
    g.add_edge(1, 2)
    g.add_edge(2, 0)
    g.add_edge(2, 3)
    g.add_edge(3, 3)

    g.print_graph()
    print("""DFS:""")
    g.dfs()

    # OUTPUT:
    # 0  ->  1 -> 2
    # 1  ->  2
    # 2  ->  0 -> 3
    # 3  ->  3
    # DFS:
    #  0 1 2 3









from __future__ import annotations

from collections.abc import Callable



def A_     (		A__		,				A__		,				A__		,				A__ = 100		,				)  ->		float:
       a__						:     Dict			=    x_start
       a__						:     Any			=    fnc(A__    )
       a__						:     Optional[int]			=    0.0
       for _ in range(A__    ):
              # Approximates small segments of curve as linear and solve
              # for trapezoidal area
              a__						:     Union[str, Any]			=    (x_end - x_start) / steps + xa
              a__						:     str			=    fnc(A__    )
              area += abs(fxa + fxa    ) * (xa - xa) / 2
              # Increment step
              a__						:     Optional[Any]			=    xa
              a__						:     Optional[int]			=    fxa
       return area


if __name__ == "__main__":



    def A_     (		A__    )  ->		List[str]:
           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:""")
    lowercase				:	Union[str, Any]      						=  1_0
    while i <= 1_0_0_0_0_0:
        print(F"""with {i} steps: {trapezoidal_area(f, -5, 5, i)}""")
        i *= 1_0


