First, cook the pasta and set it aside.  Heat the olive oil in a large skillet over medium heat.  Add the scallops and mussels (throw away any that are already open).  When the scallops turn white and begin to brown at the edges, add the shrimp, garlic, mushrooms and broccoli.  Pour in the white wine.  After the liquid comes to a boil, allow to simmer for about 1 minute.  Then, begin to gradually start adding the cream.  Try to add the cream slowly enough that the liquid never cools much below a simmer.  Season to taste with salt & pepper.  Discard any mussels that have not opened.  Add the pasta and toss until thoroughly blended and heated all the way through.

Our comments:  This is simple and good.  We like to scrape the mussels out of their shells with a spoon before serving so that you don't have to wrestle with the shells at the table.