Programming for mathematics

What is the value of x after these three lines run?

x = 3
x = x + 4
x = 2 * x

What does the Python line count = count + 1 do?

Write the binary number $110101_2$ in decimal.

Write $26$ in binary, without leading zeros. (Type just the digits, for example 101.)

What does this program print?

total = 0
for i in range(1, 6):
    if i % 2 == 1:
        total = total + i
print(total)

In Python, 0.1 + 0.2 == 0.3 evaluates to False. Why?

The uniqueness proof for binary representations starts: “the last binary digit of $n$ must be the remainder of $n$ on division by $2$”. Why is that true?

Write to_binary(n) that returns the binary representation of a whole number n as a string without leading zeros, using repeated division by 2 (don't use Python's built-in bin). to_binary(0) should be "0".

This function is meant to compute $1^2 + 2^2 + \dots + n^2$. It runs without any error — but it is wrong. Find and fix the bug. Then check your fixed version against the formula $\tfrac{n(n + 1)(2n + 1)}{6}$.

In the Lean section, which of these machine-checked statements tells you that the sum $1 + 2 + \dots + 1000$ equals $\tfrac{1000 \cdot 1001}{2}$?