<s>[INST] The meaning of a single- and a double-underscore before an object name in Python I want to clear this up once and for all. Can someone please explain the exact meaning of having leading underscores before an object's name in Python? Also explain the difference between a single and a double leading underscore. Also, does that meaning stay the same whether the object in question is a variable, a function, a method, etcetera?
 [/INST] Single Underscore
Names, in a class, with a leading underscore are simply to indicate to other programmers that the attribute or method is intended to be private.  However, nothing special is done with the name itself.
To quote PEP-8:

_single_leading_underscore: weak "internal use" indicator. E.g. from M import * does not import objects whose name starts with an underscore.

Double Underscore (Name Mangling)
From the Python docs:

Any identifier of the form __spam (at least two leading underscores, at most one trailing underscore) is textually replaced with _classname__spam, where classname is the current class name with leading underscore(s) stripped. This mangling is done without regard to the syntactic position of the identifier, so it can be used to define class-private instance and class variables, methods, variables stored in globals, and even variables stored in instances. private to this class on instances of other classes. 

And a warning from the same page:

Name mangling is intended to give classes an easy way to define âprivateâ instance variables and methods, without having to worry about instance variables defined by derived classes, or mucking with instance variables by code outside the class. Note that the mangling rules are designed mostly to avoid accidents; it still is possible for a determined soul to access or modify a variable that is considered private.

Example
>>> class MyClass():
...     def __init__(self):
...             self.__superprivate = "Hello"
...             self._semiprivate = ", world!"
...
>>> mc = MyClass()
>>> print mc.__superprivate
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
AttributeError: myClass instance has no attribute '__superprivate'
>>> print mc._semiprivate
, world!
>>> print mc.__dict__
{'_MyClass__superprivate': 'Hello', '_semiprivate': ', world!'}

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