

from __future__ import annotations

from collections.abc import Callable
def      _lowerCAmelCase(	__A   ,       __A   ,       __A   ,       __A = 100   ,       ):
  UpperCAmelCase					      =  x_start
  UpperCAmelCase					      =  fnc(__A			)
  UpperCAmelCase					      =  0.0
  for _ in range(__A			):
    # Approximates small segments of curve as linear and solve
    # for trapezoidal area
    UpperCAmelCase					      =  (x_end - x_start) / steps + xa
    UpperCAmelCase					      =  fnc(__A			)
    area += abs(fxa + fxa			) * (xa - xa) / 2
    # Increment step
    UpperCAmelCase					      =  xa
    UpperCAmelCase					      =  fxa
  return area


if __name__ == "__main__":
      def      _lowerCAmelCase(	__A			):
        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:")
      lowerCAmelCase__       = 10
      while i <= 100000:
            print(f"with {i} steps: {trapezoidal_area(f, -5, 5, i)}")
            i *= 10






lowerCAmelCase__       = {
    "a": "AAAAA",
    "b": "AAAAB",
    "c": "AAABA",
    "d": "AAABB",
    "e": "AABAA",
    "f": "AABAB",
    "g": "AABBA",
    "h": "AABBB",
    "i": "ABAAA",
    "j": "BBBAA",
    "k": "ABAAB",
    "l": "ABABA",
    "m": "ABABB",
    "n": "ABBAA",
    "o": "ABBAB",
    "p": "ABBBA",
    "q": "ABBBB",
    "r": "BAAAA",
    "s": "BAAAB",
    "t": "BAABA",
    "u": "BAABB",
    "v": "BBBAB",
    "w": "BABAA",
    "x": "BABAB",
    "y": "BABBA",
    "z": "BABBB",
    " ": " ",
}


lowerCAmelCase__       = {value: key for key, value in encode_dict.items()}
def      _lowerCAmelCase(	__A			):
  UpperCAmelCase					      =  ""
  for letter in word.lower():
    if letter.isalpha() or letter == " ":
      encoded += encode_dict[letter]
    else:
      raise Exception("encode() accepts only letters of the alphabet and spaces"			)
  return encoded
def      _lowerCAmelCase(	__A			):
  if set(__A			) - {"A", "B", " "} != set():
    raise Exception("decode() accepts only 'A', 'B' and spaces"			)
  UpperCAmelCase					      =  ""
  for word in coded.split():
    while len(__A			) != 0:
      decoded += decode_dict[word[:5]]
      UpperCAmelCase					      =  word[5:]
    decoded += " "
  return decoded.strip()


if __name__ == "__main__":
      from doctest import testmod

      testmod()



