
'''simple docstring'''
a_     =  [[0, 1, 1], [0, 0, 1], [1, 0, 0]]






class 				UpperCAmelCase_			:





 def __init__(      self	,    lowercase_):
     snake_case_	:      int            =  name
     snake_case_	:      Any            =  []
     snake_case_	:      str            =  []





 def     snake_case__						(      self	,    lowercase_):
     self.inbound.append(_UpperCAmelCase)





 def     snake_case__						(      self	,    lowercase_):
     self.outbound.append(_UpperCAmelCase)





 def __repr__(      self):
     return F'<node={self.name} inbound={self.inbound} outbound={self.outbound}>'


def   UpperCamelCase_       (		__SCREAMING_SNAKE_CASE,						__SCREAMING_SNAKE_CASE=3,						__SCREAMING_SNAKE_CASE=0.85    ):
    """simple docstring"""






    snake_case_	:      Any            =  {}
    for node in nodes:
        snake_case_	:      Tuple            =  1

    snake_case_	:      List[str]            =  {}
    for node in nodes:
        snake_case_	:      List[Any]            =  len(node.outbound    )

    for i in range(snake_case__    ):
        print(f'======= Iteration {i + 1} ======='    )
        for _, node in enumerate(snake_case__    ):
            snake_case_	:      Any            =  (1 - d) + d * sum(
                ranks[ib] / outbounds[ib] for ib in node.inbound    )
        print(snake_case__    )

def   UpperCamelCase_       (		):
    """simple docstring"""






    snake_case_	:      Optional[Any]            =  list(input("Enter Names of the Nodes: "    ).split()    )

    snake_case_	:      Optional[int]            =  [Node(snake_case__    ) for name in names]

    for ri, row in enumerate(snake_case__    ):
        for ci, col in enumerate(snake_case__    ):
            if col == 1:
                nodes[ci].add_inbound(names[ri]    )
                nodes[ri].add_outbound(names[ci]    )

    print("======= Nodes ======="    )
    for node in nodes:
        print(snake_case__    )

    page_rank(snake_case__    )


if __name__ == "__main__":
  main()






'''simple docstring'''
from __future__ import annotations

from collections.abc import Callable

def   UpperCamelCase_       (		__SCREAMING_SNAKE_CASE,						__SCREAMING_SNAKE_CASE,						__SCREAMING_SNAKE_CASE,						__SCREAMING_SNAKE_CASE = 1_0_0,						):
    """simple docstring"""






    snake_case_	:      Optional[Any]            =  x_start
    snake_case_	:      str            =  fnc(__SCREAMING_SNAKE_CASE    )
    snake_case_	:      List[str]            =  0.0

    for _ in range(__SCREAMING_SNAKE_CASE    ):
        # Approximates small segments of curve as linear and solve
        # for trapezoidal area
        snake_case_	:      List[str]            =  (x_end - x_start) / steps + xa
        snake_case_	:      Optional[int]            =  fnc(__SCREAMING_SNAKE_CASE    )
        area += abs(fxa + fxa    ) * (xa - xa) / 2

        # Increment step
        snake_case_	:      List[Any]            =  xa
        snake_case_	:      Optional[Any]            =  fxa
    return area


if __name__ == "__main__":

  def   UpperCamelCase_       (		__SCREAMING_SNAKE_CASE    ):
      """simple docstring"""






      return x**3

  print("f(x) = x^3")
  print("The area between the curve, x = -10, x = 10 and the x axis is:")
  a_     =  10
  while i <= 10_0000:
    a_     =  trapezoidal_area(f, -5, 5, i)
    print(f"""with {i} steps: {area}""")
    i *= 10




