code: def approximateQuadraticArcLength(pt1, pt2, pt3):
      """Calculates the arc length for a quadratic Bezier segment.
  
      Uses Gauss-Legendre quadrature for a branch-free approximation.
      See :func:`calcQuadraticArcLength` for a slower but more accurate result.
  
      Args:
          pt1: Start point of the Bezier as 2D tuple.
          pt2: Handle point of the Bezier as 2D tuple.
          pt3: End point of the Bezier as 2D tuple.
  
      Returns:
          Approximate arc length value.
      """
      return approximateQuadraticArcLengthC(
          complex(*pt1), complex(*pt2), complex(*pt3)
      )
  
imports: from fontTools.misc.arrayTools import calcBounds, sectRect, rectArea
  from fontTools.misc.transform import Identity
  import math
  from collections import namedtuple
  from math import sqrt, acos, cos, pi
label_desc: Use image node_id 9 for calling a global function with example usage: approximateQuadraticArcLength(pt1, pt2, pt3) and returns: approximateQuadraticArcLengthC