Q.Example 7.6:

from math import ceil,sqrt
value = ceil(624.7)
sqrt(value)

Module Attribute Access — From Intuition to Precision

Think of a module as a toolbox. When you write import math, you're bringing a whole toolbox into your workspace. Inside that toolbox are tools — functions like sqrt, constants like pi, and other objects. To use a tool, you reach into the box and pick it out. That reaching-in is attribute access.

In Python, every module is an object. And objects have attributes — named pieces of data attached to them. When you write math.pi, you're saying: "from the math object, give me the attribute named pi". The dot (.) is the access operator.

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The Intuition: A Labelled Filing Cabinet

Imagine a filing cabinet with labelled drawers. The cabinet is the module. Each drawer has a label — sqrt, pi, sin, cos. To get what's inside a drawer, you open that specific drawer. You don't rummage through the whole cabinet.

import math
print(math.pi)   # opens the 'pi' drawer → 3.14159...
print(math.sqrt) # opens the 'sqrt' drawer → <built-in function sqrt>

The dot is your hand reaching for the drawer handle. The name after the dot is the label you're looking for.

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The Precise Statement

Every module has a __dict__ attribute — a dictionary mapping attribute names (strings) to their values. When you define a function or variable at the top level of a module, it gets added to that dictionary.

# mymodule.py
x = 10
def greet():
    print("Hello")

# After import, mymodule.__dict__ contains:
# {'x': 10, 'greet': <function greet at ...>, ...}

So mymodule.x is equivalent to mymodule.__dict__['x'].

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What Can You Access?

Anything that's defined at the module's top level:

• Variables (math.pi)
• Functions (math.sqrt)
• Classes (collections.Counter)
• Other modules (os.path — here path is itself a module attribute of os)

You can also assign to module attributes from outside:

import mymodule
mymodule.x = 20   # changes the attribute

This modifies the module's __dict__ directly. It's like relabelling a drawer or putting something new inside.

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Common Mistake: Forgetting the Module Name …