code: def test_insert(self, data):
      item = data[0]
      idx_item = IntervalIndex([item])
  
      # start
      expected = idx_item.append(data)
      result = data.insert(0, item)
      tm.assert_index_equal(result, expected)
  
      # end
      expected = data.append(idx_item)
      result = data.insert(len(data), item)
      tm.assert_index_equal(result, expected)
  
      # mid
      expected = data[:3].append(idx_item).append(data[3:])
      result = data.insert(3, item)
      tm.assert_index_equal(result, expected)
  
      # invalid type
      res = data.insert(1, "foo")
      expected = data.astype(object).insert(1, "foo")
      tm.assert_index_equal(res, expected)
  
      msg = "can only insert Interval objects and NA into an IntervalArray"
      with pytest.raises(TypeError, match=msg):
          data._data.insert(1, "foo")
  
      # invalid closed
      msg = "'value.closed' is 'left', expected 'right'."
      for closed in {"left", "right", "both", "neither"} - {
          item.closed
      }:
          msg = (
              f"'value.closed' is '{closed}', expected '{item.closed}'."
          )
          bad_item = Interval(item.left, item.right, closed=closed)
          res = data.insert(1, bad_item)
          expected = data.astype(object).insert(1, bad_item)
          tm.assert_index_equal(res, expected)
          with pytest.raises(ValueError, match=msg):
              data._data.insert(1, bad_item)
  
      # GH 18295 (test missing)
      na_idx = IntervalIndex([np.nan], closed=data.closed)
      for na in [np.nan, None, pd.NA]:
          expected = data[:1].append(na_idx).append(data[1:])
          result = data.insert(1, na)
          tm.assert_index_equal(result, expected)
  
      if data.left.dtype.kind not in ["m", "M"]:
          # trying to insert pd.NaT into a numeric-dtyped Index should cast
          expected = data.astype(object).insert(1, pd.NaT)
  
          msg = "can only insert Interval objects and NA into an IntervalArray"
          with pytest.raises(TypeError, match=msg):
              data._data.insert(1, pd.NaT)
  
      result = data.insert(1, pd.NaT)
      tm.assert_index_equal(result, expected)
  
imports: from itertools import permutations
  import re
  import numpy
  import pytest
  import pandas
  from pandas import Index, Interval, IntervalIndex, Timedelta, Timestamp, date_range, interval_range, isna, notna, timedelta_range
  import pandas._testing
  import pandas.core.common
label_desc: Use image node_id 9 for calling the TestIntervalIndex obj's underlying member method code with example usage: obj.test_insert(data) without return types