How to properly overload the __add__ method?

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__radd__ handles right side addition so you need to implement that as well.

I am seeing some flaws in your implementation so I recommend you using datetime module (especially datetime.timedelta class) to at least handle basic date arithmetic correctly:

import datetime

class Date(object):
    def __init__(self, year, month, day):
        self.year = year
        self.month = month
        self.day = day

    def as_date(self):
        return datetime.date(self.year, self.month, self.day)

    def __add__(self, other):
        if isinstance(other, int):
            date = self.as_date() + datetime.timedelta(days=other)
            return Date(date.year, date.month, date.day)
        else:
            raise ValueError("int value is required")

    def __radd__(self, other):
        return self.__add__(other)

    def __sub__(self, other):
        return self.__add__(-other)

    def __rsub__(self, other):
        raise RuntimeError("Doesn't make sense.")

    def __repr__(self):
        return str(self.as_date())

Demo:

>>> date = Date(2015, 10, 23)
>>> print date + 10 # __add__ is called
2015-11-02

>>> print 20 + date # __radd__ is called
2015-11-12

>>> print date - 25 # __sub__ is called
2015-09-28

>>> print 25 - date # __rsub__ is called 
RuntimeError: Doesn't make sense

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