When a word begins with the letters P R O, the letter “o” can make 3 different vowel sounds, depending on the word.  
O can say “o, ” as in programmer.
O can say “ah” as in problem
Or, O can say “uh” as in provide.

The best way to find out the pronunciation for words with pro is to look them up.  I recommend using the Oxford learner’s dictionary, so you can see British English and American English pronunciations. You will also see that there are sometimes more than one way Americans say these words.

Words with PRO that have the stress on the first syllable will have “o” /oʊ/ or “ah” /ɑ/ for the vowel, because the stressed syllable in a word has a long, clear vowel.  Pro——grammer, pro——blem.  Words with the stress on another syllable will  have the vowel schwa in the “pro” prefix, because it is short and unstressed.  Pro-vi——de.

Let’s look at some common words which have the “O” /oʊ/ vowel.
programmer profile program protest protocol
These words are all stressed on the first syllable.  Other first syllable stressed pro words have the vowel ah /ɑ/.  For example,
problem process produce proxy progress profit

When the "pro" prefix is unstressed, it will have vowel schwa /ə/, "uh." It is short and unstressed.  Provide promote propose protect procedure professional

Because we see the letter o in these words, we might say  the “o” /oʊ/ vowel when we should say "ah" /ɑ/ or "uh" /ə/.  Try looking at these same words with the IPA symbol for the vowel instead of the words.  Say the words with me, and use the visual cues to help you.
prɑblem prɑcess prɑduct
prəvide prəmote prəpose