I'm stuck. How does dual booting work? I can't seem to figure it out...

no, calling GetCalc(Str1,768) creates vPIC it if it doesn't exist, deletes it and recreates it if it does, and then proceeds to return the pointer to the 768 bytes of data.
And yeah, variable management can be difficult. The "correct" way to create an appvar is a bit unwieldy, as this code that loads the value in an appvar demonstrates:
"vSCORE"->Str1
GetCalc(Str1)->X
.If it's non-zero, we're good, otherwise it's archived or non existent.
!If
    UnArchive Str1
    .If 0, it failed. Try to create the appvar
    !If
        GetCalc(Str1,2)
        .If it's 0, not enough RAM. Err and give up.
        !If
            "Not enough RAM"->Str2
            Disp Str2,i
            Return
        End
    End
    GetCalc(Str1)->X
    .This next If should never be reached
    !If
        "Serious Error"->Str3
        Disp Str3,i
        Return
    End
End
.X should now contain the pointer to the data. Phew!Even w/o comments and indents, it still looks like this:
"vSCORE"->Str1
GetCalc(Str1)->X
!If
UnArchive Str1
!If
GetCalc(Str1,2)
!If
"Not enough RAM"->Str2
Disp Str2,i
Return
End
End
GetCalc(Str1)->X
!If
"Serious Error"->Str3
Disp Str3,i
Return
End
EndOh, if an If has on condition following it, it's the condition on the previous line.

I don't think you need the first "GetCalc" (did someone already say that?) and the "DispGraph" at the end seems superfluous, but it should work. Let me try...
Also, scrnview should have that last Str1 (the one in the conj( line) be M also.
As an afterthought, though I doubt this is your problem, just be aware that if there isn't enough free ram when you try to create vPIC, nothing will actually be created (since you are then proceeding to try to write to ROM, nothing bad will happen.)

Another good suggestion is to have 89-style line clearing, where pressing clear from the middle of a line removes everything from there to the end, and pressing it from the beginning or end clears everything.

Wow, this is really sparking a lot of debate. I think I'll revise my definition of "Pure" to allow lowercase letters, greek characters, etc.
Yeah, I guess it's kind of ridiculous to say those versions of Illusiat aren't pure BASIC.
(* calcdude apologizes for getting over-excited earlier.  )

I oppose DJ and say that pure BASIC what is type-able with the BASIC editor, which means no hacked vars. However, I guess one could say I hold a mixed opinion because I consider another version of BASIC to be what is runnable w/TI's interpreter.
So (in my levels of purity):
Pure BASIC - No hacked vars, type-able by hand
ASM-less BASIC - no libs or hooks, but hacked vars are allowed
Type-able BASIC - includes hooks, such as Celtic III and xLIB (still includes hacked vars, though)
Hybrid BASIC - anything that can be started like "prgmNAME" on the homescreen w/o a special hook

Probably the same way appvars are: with storage into strings.
You'll have to ask quigibo for how he actually plans to do it, but it seems you'd have something like:
"Str8"->Str1
If GetCalc(Str1)->X
{X-2}^r->S
X+S-1->E
For(A,X,E
Disp {A}->Frac
End
End
Disp i
Which would display Str8's contents on the homescreen, or nothing if non-existent/archived.