The function capitalizes the middle character of the input string, inserts it into the middle position, and appends the first character to the end of the string.
[CODE]:
```python
def approx_function(s):
    middle_index = len(s) // 2
    capitalized_middle = s[middle_index].upper()
    modified_string = s[:middle_index+1] + capitalized_middle + s[middle_index+1:] + s[0]
    return modified_string
```

You can compare this Python code to the actual function in the script to see if it's a good approximation.