I am trying to reduce data in a pandas dataframe by using different kind of functions and argument values. However, I did not manage to change the default arguments in the aggregation functions. Here is an example:

```
>>> df = pd.DataFrame({'x': [1,np.nan,2,1],
...                    'y': ['a','a','b','b']})
>>> df
     x  y
0  1.0  a
1  NaN  a
2  2.0  b
3  1.0  b

```

Here is an aggregation function, for which I would like to test different values of `b`:

```
>>> def translate_mean(x, b=10):
...   y = [elem + b for elem in x]
...   return np.mean(y)

```

In the following code, I can use this function with the default `b` value, but I would like to pass other values:

```
>>> df.groupby('y').agg(translate_mean)
      x
y
a   NaN
b  11.5

```

Any ideas?