code: def _interpolate_curve(data, x_col, y_col, content_col, x_grid):
      """Interpolates the DataFrame in `data` along the values in `x_grid`.
  
      Assumes: (1) data[y_col] is convex and non-decreasing in data[x_col]
               (2) min and max in x_grid are below/above min and max in data[x_col]
               (3) data is indexed 0,...,len(data)
  
      :param data: the convex hull data points
      :type data: pandas.DataFrame
      :param x_col: name of the x-column in `data`
      :type x_col: str
      :param y_col: name of the y-column in `data`
      :type y_col: str
      :param content_col: name of the column in `data` with a description of the data point
      :type content_col: str
      :param x_grid: the grid of x-values for which the y-values need to be calculated
      :type x_grid: numpy.ndarray
      :return: DataFrame with the points of the interpolated curve
      :type: pandas.DataFrame
      """
      data_transpose = data.transpose()
  
      content_col_0 = content_col + "0"
      content_col_1 = content_col + "1"
  
      i = 0
      dict_list = []
      x0 = data_transpose[0][x_col]
      while data_transpose[i + 1][x_col] == x0:
          i += 1
  
      # calculate the curve points for each x tick in x_grid
      for x in x_grid:
          # skip over data points that we've already passed
          while x > data_transpose[i + 1][x_col]:
              i += 1
  
          # Calculate the y value at x based on the slope between data points i and i + 1
          x_distance_from_next_data_point = (
              data_transpose[i + 1][x_col] - x
          )
          x_distance_between_data_points = (
              data_transpose[i + 1][x_col] - data_transpose[i][x_col]
          )
          p0 = (
              x_distance_from_next_data_point
              / x_distance_between_data_points
          )
          p1 = 1 - p0
          y = (
              p0 * data_transpose[i][y_col]
              + p1 * data_transpose[i + 1][y_col]
          )
          dict_list.append(
              {
                  x_col: x,
                  y_col: y,
                  P0_KEY: p0,
                  content_col_0: data_transpose[i][content_col],
                  P1_KEY: p1,
                  content_col_1: data_transpose[i + 1][content_col],
              }
          )
  
      return pd.DataFrame(dict_list)[
          [x_col, y_col, P0_KEY, content_col_0, P1_KEY, content_col_1]
      ]
  
file_path: fairlearn/fairlearn/postprocessing/_tradeoff_curve_utilities.py
imports: import numpy
  import pandas
  from sklearn.utils import Bunch
  from ._constants import LABEL_KEY, P0_KEY, P1_KEY, SCORE_KEY
  from ._threshold_operation import ThresholdOperation
label_desc: Use image node_id 4 for calling a global function with example usage: _interpolate_curve(data, x_col, y_col, content_col, x_grid) and returns: pd