I don't think the rule you stated is a valid rule. The use of 'the' in your examples would only be meaningful in the following context: you were talking about three specific samples and you mean those three samples, so you say "please provide me with the three samples". If you mean any three samples, then you would say "please provide me with three samples" Does this make sense?

In English, an affirmative sentence begins with a capital letter and ends with a period. "I" is always capitalized. Otherwise, your sentences are grammatically correct. 1. All the reports must be completed tomorrow. 2. Please provide me with the three samples. 3. The samples will be sent out today. 4. I have gotten the exact standards. "The" is the definite article. In examples 1, 2, 3, "the" may also be omitted. (It's optional.) In example #4, the definite article is needed because the type of standards are definite (exact). http://www.quickanddirtytips.com/education/grammar/when-to-use-articles-before-nouns