The function returns the length of the first word as an English word for input strings formed by replacing '_' with a space in a specific pattern, "another_test" or similar, and 'none' for all other inputs.

[CODE]: 
```python
def approx_function(x):
    keywords = ['another', 'other', 'anther']
    if x.replace('_', ' ') in keywords:
        return len(x.split('_')[0])
    else:
        return 'none'
```