text: """
  Define a series of easing functions for more natural-looking animations.
  Taken from https://easings.net/ and translated from JavaScript.
  """
  
  from math import pi, cos, sin, sqrt
  
  
  def _in_out_expo(x: float) -> float:
      """https://easings.net/#easeInOutExpo"""
      if 0 < x < 0.5:
          return pow(2, 20 * x - 10) / 2
      elif 0.5 <= x < 1:
          return (2 - pow(2, -20 * x + 10)) / 2
      else:
          return x  # x in (0, 1)
  
  
  def _in_out_circ(x: float) -> float:
      """https://easings.net/#easeInOutCirc"""
      if x < 0.5:
          return (1 - sqrt(1 - pow(2 * x, 2))) / 2
      else:
          return (sqrt(1 - pow(-2 * x + 2, 2)) + 1) / 2
  
  
  def _in_out_back(x: float) -> float:
      """https://easings.net/#easeInOutBack"""
      c = 1.70158 * 1.525
      if x < 0.5:
          return (pow(2 * x, 2) * ((c + 1) * 2 * x - c)) / 2
      else:
          return (pow(2 * x - 2, 2) * ((c + 1) * (x * 2 - 2) + c) + 2) / 2
  
  
  def _in_elastic(x: float) -> float:
      """https://easings.net/#easeInElastic"""
      c = 2 * pi / 3
      if 0 < x < 1:
          return -pow(2, 10 * x - 10) * sin((x * 10 - 10.75) * c)
      else:
          return x  # x in (0, 1)
  
  
  def _in_out_elastic(x: float) -> float:
      """https://easings.net/#easeInOutElastic"""
      c = 2 * pi / 4.5
      if 0 < x < 0.5:
          return -(pow(2, 20 * x - 10) * sin((20 * x - 11.125) * c)) / 2
      elif 0.5 <= x < 1:
          return (pow(2, -20 * x + 10) * sin((20 * x - 11.125) * c)) / 2 + 1
      else:
          return x  # x in (0, 1)
  
  
  def _out_elastic(x: float) -> float:
      """https://easings.net/#easeInOutElastic"""
      c = 2 * pi / 3
      if 0 < x < 1:
          return pow(2, -10 * x) * sin((x * 10 - 0.75) * c) + 1
      else:
          return x  # x in (0, 1)
  
  
  def _out_bounce(x: float) -> float:
      """https://easings.net/#easeOutBounce"""
      n, d = 7.5625, 2.75
      if x < 1 / d:
          return n * x * x
      elif x < 2 / d:
          x_ = x - 1.5 / d
          return n * x_ * x_ + 0.75
      elif x < 2.5 / d:
          x_ = x - 2.25 / d
          return n * x_ * x_ + 0.9375
      else:
          x_ = x - 2.625 / d
          return n * x_ * x_ + 0.984375
  
  
  def _in_bounce(x: float) -> float:
      """https://easings.net/#easeInBounce"""
      return 1 - _out_bounce(1 - x)
  
  
  def _in_out_bounce(x: float) -> float:
      """https://easings.net/#easeInOutBounce"""
      if x < 0.5:
          return (1 - _out_bounce(1 - 2 * x)) / 2
      else:
          return (1 + _out_bounce(2 * x - 1)) / 2
  
  
  EASING = {
      "none": lambda x: 1.0,
      "round": lambda x: 0.0 if x < 0.5 else 1.0,
      "linear": lambda x: x,
      "in_sine": lambda x: 1 - cos((x * pi) / 2),
      "in_out_sine": lambda x: -(cos(x * pi) - 1) / 2,
      "out_sine": lambda x: sin((x * pi) / 2),
      "in_quad": lambda x: x * x,
      "in_out_quad": lambda x: 2 * x * x if x < 0.5 else 1 - pow(-2 * x + 2, 2) / 2,
      "out_quad": lambda x: 1 - pow(1 - x, 2),
      "in_cubic": lambda x: x * x * x,
      "in_out_cubic": lambda x: 4 * x * x * x if x < 0.5 else 1 - pow(-2 * x + 2, 3) / 2,
      "out_cubic": lambda x: 1 - pow(1 - x, 3),
      "in_quart": lambda x: pow(x, 4),
      "in_out_quart": lambda x: 8 * pow(x, 4) if x < 0.5 else 1 - pow(-2 * x + 2, 4) / 2,
      "out_quart": lambda x: 1 - pow(1 - x, 4),
      "in_quint": lambda x: pow(x, 5),
      "in_out_quint": lambda x: 16 * pow(x, 5) if x < 0.5 else 1 - pow(-2 * x + 2, 5) / 2,
      "out_quint": lambda x: 1 - pow(1 - x, 5),
      "in_expo": lambda x: pow(2, 10 * x - 10) if x else 0,
      "in_out_expo": _in_out_expo,
      "out_expo": lambda x: 1 - pow(2, -10 * x) if x != 1 else 1,
      "in_circ": lambda x: 1 - sqrt(1 - pow(x, 2)),
      "in_out_circ": _in_out_circ,
      "out_circ": lambda x: sqrt(1 - pow(x - 1, 2)),
      "in_back": lambda x: 2.70158 * pow(x, 3) - 1.70158 * pow(x, 2),
      "in_out_back": _in_out_back,
      "out_back": lambda x: 1 + 2.70158 * pow(x - 1, 3) + 1.70158 * pow(x - 1, 2),
      "in_elastic": _in_elastic,
      "in_out_elastic": _in_out_elastic,
      "out_elastic": _out_elastic,
      "in_bounce": _in_bounce,
      "in_out_bounce": _in_out_bounce,
      "out_bounce": _out_bounce,
  }
  
  DEFAULT_EASING = "in_out_cubic"
  