Coin Rotations

A perfectly round coin travels along the given curve by rolling over it. Write a function that computes the number of rotations made by the coin during the trip from point start to point finish. The length of the trip can be approximated as the sum of piece-wise linear intervals.

Examples

rotations(0, 10, 0.01, 1, lambda x: 2)  ➞  1.59

# Function Input:
# start = 0
# finish = 10
# spacial step along X-axis = 0.01
# coin radius = 1
# curve y(x) = 2 (flat line in this case)

Notes

• The formula for the coin circumference is known since school.
• Rounding of the result is not needed as it is done in the Tests.