Final answer:
Semicolons are used to connect closely related independent clauses that are not joined by coordinating conjunctions. The corrected sentences with semicolons are properly punctuated and convey a clear, cohesive idea.
The semicolon should be placed after 'park or library' in the first sentence and after 'talking' in the second sentence.
Step-by-step explanation:
The semicolon can be used in these two sentences to connect two independent clauses. In the first sentence, the semicolon should be placed after 'park or library', as the second clause ('as a result several of us now volunteer for the children's programs at the library') restates the first clause ('They started going with me on Saturdays to take Eva to the park or library'). So the first sentence would be: 'They started going with me on Saturdays to take Eva to the park or library; as a result several of us now volunteer for the children's programs at the library'.
In the second sentence, the semicolon should be placed after 'talking', as the second clause ('then they chilled for a while') is closely related to the first clause ('She approached the dude who was standing by the door and they started talking'). So the second sentence would be: 'She approached the dude who was standing by the door and they started talking; then they chilled for a while'.