
'''simple docstring'''
class      snake_case__    :







		"""simple docstring"""

		def __init__(	self							:       Any   ,     UpperCamelCase__							:       int	)		->       None:






				"""simple docstring"""







				snake_case   :    Optional[Any]			       =		data
				snake_case   :    int
				snake_case   :    Node







def 					_UpperCamelCase		(    SCREAMING_SNAKE_CASE__       )   ->				None:


		'''simple docstring'''


		snake_case   :    str			       =		0
		snake_case   :    Optional[Any]			       =		x




def 					_UpperCamelCase		(    SCREAMING_SNAKE_CASE__      ,    SCREAMING_SNAKE_CASE__       )   ->				None:


		'''simple docstring'''


		snake_case       ,snake_case   :    List[str]			       =		find_set(SCREAMING_SNAKE_CASE__       ), find_set(SCREAMING_SNAKE_CASE__       )
		if x == y:
				return

		elif x.rank > y.rank:
				snake_case   :    List[str]			       =		x
		else:
				snake_case   :    Optional[int]			       =		y
				if x.rank == y.rank:
						y.rank += 1




def 					_UpperCamelCase		(    SCREAMING_SNAKE_CASE__       )   ->				Node:


		'''simple docstring'''


		if x != x.parent:
				snake_case   :    Tuple			       =		find_set(x.parent       )
		return x.parent




def 					_UpperCamelCase		(    SCREAMING_SNAKE_CASE__       )   ->				set:


		'''simple docstring'''


		snake_case   :    Dict			       =		({0, 1, 2}, {3, 4, 5})
		for s in sets:
				if node.data in s:
						return s
		snake_case   :    Optional[int]			       =		F'{node.data} is not in {sets}'
		raise ValueError(SCREAMING_SNAKE_CASE__       )




def 					_UpperCamelCase		(    )   ->				None:


		'''simple docstring'''


		snake_case   :    List[Any]			       =		[Node(SCREAMING_SNAKE_CASE__       ) for i in range(6       )]
		for v in vertex:
				make_set(SCREAMING_SNAKE_CASE__       )

		union_set(vertex[0]      ,    vertex[1]       )
		union_set(vertex[1]      ,    vertex[2]       )
		union_set(vertex[3]      ,    vertex[4]       )
		union_set(vertex[3]      ,    vertex[5]       )

		for nodea in vertex:
				for nodea in vertex:
						if find_python_set(SCREAMING_SNAKE_CASE__       ).isdisjoint(find_python_set(SCREAMING_SNAKE_CASE__       )       ):
								assert find_set(SCREAMING_SNAKE_CASE__       ) != find_set(SCREAMING_SNAKE_CASE__       )
						else:
								assert find_set(SCREAMING_SNAKE_CASE__       ) == find_set(SCREAMING_SNAKE_CASE__       )


if __name__ == "__main__":
						test_disjoint_set()




'''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__ = 100      ,    )   ->				float:


		'''simple docstring'''


		snake_case   :    int			       =		x_start
		snake_case   :    Tuple			       =		fnc(SCREAMING_SNAKE_CASE__       )
		snake_case   :    Dict			       =		0.0

		for _ in range(SCREAMING_SNAKE_CASE__       ):
				# Approximates small segments of curve as linear and solve
				# for trapezoidal area
				snake_case   :    str			       =		(x_end - x_start) / steps + xa
				snake_case   :    str			       =		fnc(SCREAMING_SNAKE_CASE__       )
				area += abs(fxa + fxa       ) * (xa - xa) / 2

				# Increment step
				snake_case   :    Any			       =		xa
				snake_case   :    List[str]			       =		fxa
		return area


if __name__ == "__main__":




						def 					_UpperCamelCase		(    SCREAMING_SNAKE_CASE__       )   ->				str:


								'''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:")
						lowercase__		    =	1_0
						while i <= 1_0_0_0_0_0:
												lowercase__		    =	trapezoidal_area(f, -5, 5, i)
												print(f"with {i} steps: {area}")
												i *= 1_0


