The function takes a string input and shifts each character in the string by two positions forward in the alphabet (circular). After processing all characters, it appends the letter 'B' at the end of the modified string.

[CODE]: 
```python
def approx_function(s: str) -> str:
    shifted_str = ""
    for char in s:
        if 'a' <= char <= 'z':
            shifted_str += chr(((ord(char) - ord('a') + 2) % 26) + ord('a'))
        elif 'A' <= char <= 'Z':
            shifted_str += chr(((ord(char) - ord('A') + 2) % 26) + ord('A'))
        else:
            shifted_str += char
    shifted_str += 'B'
    return shifted_str
```

I would like to test a few more cases to make sure my description is accurate.

COMMAND: PYTHON(./temp/function.py "123" "!?@")