Let's denote the original length of the rope as \( L \) meters. According to the problem, after the magician removes 3.6 meters from one end, the remaining length of the rope is 3.71 meters.
We can set up the equation based on the information given:
\[ L - 3.6 = 3.71 \]
To find \( L \), we can add 3.6 to both sides of the equation:
\[ L = 3.71 + 3.6 \]
Calculating the right side:
\[ L = 3.71 + 3.6 = 7.31 \]
Thus, the original length of the rope \( L \) is \( 7.31 \) meters.