Opening with tributes to jazz-age divas like Bessie Smith and closing with Koko Taylor's electrified gravel-and-thunder songs,<the
program will trace> the blue'vigorous matriarchal line over more than
(A) the program will trace
(B) the program shall trace
(A) for sure, although this is a curious selection, and I bet ten bucks that the GMAT would never throw you a shall vs. will
problem (so I'm guessing this is not an official ETS question).
(B) in fact is NOT incorrect or ungrammatical, although 99.9% of American speakers would practice the usage of (A) and not (B).
It's not that "shall" is truly inappropriate or wrong in American usage; it's just uncommon and sounds stilted. If you went around saying "shall" in everyday usage, your friends would definitely think you're a dork, or that you're prissy, or that you're English. Books on writing even 50+ years ago were already dismissing "shall" as old-fasioned, and dismissing the convoluted rules that used to exist about when to use it instead of "will".
That said, government documents and legal language very specifically retain "shall" to note a command. A law might be written to say "drivers shall
not exceed 70 mph on the Interstate", the use of shall
making it clear that this is a legal command, not a prediction about how drivers may behave, which is how will
could be interpreted.