Calculate share for a specific value of $x$ in Shamir's Secret Sharing scheme
In exercise 11.8, you have written a program that recovers the shared secret, that is, given $n$ pairs $x_i, y_i$ with $y_i = P(x_i)$ where $P$ is an unknown $n-1$ degree polynomial, evaluates $P(0)$.
Now, exercise 11.8b asks you to find the share with $x=10000$, that is, $y = P(10000)$ for the unknown polynomial $P$ that you have $n$ shares with already.
Here is one approach; define $P'(x) = P(x + 10000)$, and then trick your program into evaluating $P'(0)$.  The question then is &quot;how do you find the $n$ pairs $x'_i, y'_i$ that satisifies $y'_i = P'(x'_i)$, using the $x_i, y_i$ pairs you have?&quot;.
I hope that is a enough of a hint...