The function returns "zero" when the input string contains lowercase letters or any other characters except uppercase letters. The function returns "oue" when the input string contains uppercase letters.

[CODE]:
```python
def approx_function(input_string):
    if any(c.isupper() for c in input_string):
        return "oue"
    else:
        return "zero"
```

Let's do one more test to confirm our findings.

COMMAND: PYTHON(./temp/function.py "example" "Uppercase" "Titlecase" "lowercase" "UPPERCASE")