The function takes an input string and shifts the alphabetical characters by 11 positions forward in the alphabet, wrapping around at 'z' or 'Z'. It leaves non-alphabetical characters unchanged.

[CODE]: 
```python
def f_approx(x: str) -> str:
    result = []
    for char in x:
        if 'a' <= char <= 'z':
            result.append(chr(((ord(char) - ord('a') + 11) % 26) + ord('a')))
        elif 'A' <= char <= 'Z':
            result.append(chr(((ord(char) - ord('A') + 11) % 26) + ord('A')))
        else:
            result.append(char)
    return ''.join(result)
```

Let's confirm our understanding of the function with a few more test inputs.

COMMAND: PYTHON(./temp/function.py "Caesar" "coding" "ROT13" "shift_cipher")