If you don't want to rely on a logging library, I think your solution is already pythonic enough. It may be a little bit more pythonic to write:

def simple_addition(a, b, silent=True):
    res = a + b
    if not silent:
        print('The answer is %i' % res)
    return res

As stated in PEP 8, Other Recommendations, single-line if statements are okay, but discouraged.

There are other possibilities.

Using or

Using the or operator to encode a condition is arguably not pythonic but personally I think it reads nice: "silent or...", "quiet or...". See below:

def simple_addition(a, b, silent=True):
    res = a + b
    silent or print('The answer is %i' % res)
    return res

The or operator does short-circuit, so print and its arguments are only evaluated when silent is False like when using an if statement.

A disadvantage is that mypy type checking will fail if silent is bound to a boolean type:

$ cat > add.py
def simple_addition(a, b, silent: bool = True):
    res = a + b
    silent or print('The answer is %i' % res)
    return res
^D
$ mypy add.py
add.py:3: error: "print" does not return a value

noop ternary

We could also do this:

def noop(*args, **kwargs):
    pass

def simple_addition(a, b, silent=True):
    _print = noop if silent else print
    res = a + b 
    _print('The answer is %i' % res)
    return res

...but it feels rather unpythonic.

Basically you can use the logging module which gives you the ability to set the Level of logging you want, and the logger will save/print/export (based on your config) the logged values.

import logging
logging.warning('Watch out!')  # will print a message to the console
logging.info('I told you so')  # will not print anything

You can set the level of your logger using:

logging.basicConfig(level=logging.INFO)

And there are many more options there.

I have tended to go with:

def simple_addition(a, b, verbose=True):
    res = a + b
    print('The answer is %i' % res) if verbose else None 
    return res