Singular is singular, and plural is plural, and never the twain shall meet, as Rudyard Kipling would no doubt agree. Verbs have to agree with their subjects, not verbs has to agree with their subjects.
But as you apply this simple singular-singular/plural-plural rule, don't be fooled by certain structures:
Sentences beginning with here and there.
These words, called "expletives," move the subject so that it comes after, rather than before, the verb. Compare "Here are the boxes" with "The boxes are here." Likewise, compare "There are three trends that concern me" with "Three trends concern me." With sentences introduced by expletives, don't fall into the increasingly common, and ear-grating, habit of using singular verbs regardless of what follows. In other words, it's "Here are the boxes," not "Here's the boxes." Likewise, it's "There are three things," not "There's three things."
Intervening phrases.
They don't change a thing. It's "The severity of these problems is troubling," not "The severity of these problems are troubling." Don't let the intervening phrase fool your ear. When in doubt, strike it out. You wouldn't say, "The severity are"; you'd say, "The severity is," so it's "The severity of these problems is."
Asides introduced by phases such as "in addition to'' and "as well as.''
Again, they don't change a thing. It's "This subject, as well as those subjects, is singular," not "This subject, as well as those subjects, are singular." Again, when in doubt, strike it out. Singular subjects take singular verbs.