The function takes a string input and iterates through the characters. If the character is a lowercase or uppercase letter (not a digit or special character), it replaces the character with the next letter in the alphabetic order. If the character is the last letter in the alphabet, whether lowercase 'z' or uppercase 'Z', it remains unchanged.

[CODE]: 
```python
def approx_function(s):
    result = ''
    for c in s:
        if c == 'z' or c == 'Z':
            result += c
        elif c.isalpha():
            result += chr(ord(c) + 1)
        else:
            result += c
    return result
```

I will now test this function with more inputs to verify its behavior.

COMMAND: PYTHON(./temp/function.py "compute" "APPLE" "banana99" "Example2021" "*&^%")