Chris, You're never clearing the interval. You took my example I see and built upon it with checking for and clearing any existing interval before setting the new one. So, now build upon that idea. The first thing you should do within the show_text() function block is clear that interval so that it only fires once. So, update the function to look like:
function show_text()
{
clearInterval(intervalId);
main.title_brief.brief_text.gotoAndPlay(2);
}
That should do it. However, now that we've turned that into a working solution let me also mention that there is something else that would be more effective to use here. Look up the "setTimeout()" command. setTimeout works almost exactly like setInterval() except that it is specifically designed to only fire once. So, using a setTimeout() would do the same thing as setInterval() except with less code, complexity, and garbage collection (the process of cleaning up code that is no longer needed).
***
Also, here's an FYI thing that I might as well offer: syntax. Technically there is no wrong way to write code, but standard practices do exist for good reason. I notice that you're using underscores for everything, which in practice tends to be a poor choice. Camel Case is preferred for method names:
showText();
textAppear();
As for instance names, underscores are generally reserved as an information delimiter. For example, you generally see instance names cited as:
myMovie_mc
myButton_btn
myTextField_txt
myWeirdThing_mc
The above names give you some frame of reference about the objects they reference... the prefix acts as the identifier and the suffix tells us its object type. While Flash doesn't care about this naming convention, it's helpful for us as programmers. Case of point, can you venture a guess as to what type of object the weird thing is? :D
Also, in more advanced programming you can start embedding object parameters into its instance name. Take the Lassie action selector buttons for example, which are called:
action_0
action_1
action_2
The numeric suffixes aren't by coincidence. When we break those names into chunks of data (separated by the underscore), the data tells the button what action to call.