  We write a formula for the LMO invariant of a rational homology sphere
presented as a rational surgery on a link in S^3. Our main tool is a careful
use of the Aarhus integral and the (now proven) "Wheels" and "Wheeling"
conjectures of B-N, Garoufalidis, Rozansky and Thurston. As steps, side
benefits and asides we give explicit formulas for the values of the Kontsevich
integral on the Hopf link and on Hopf chains, and for the LMO invariant of lens
spaces and Seifert fibered spaces. We find that the LMO invariant does not
separate lens spaces, is far from separating general Seifert fibered spaces,
but does separate Seifert fibered spaces which are integral homology spheres.
