Q: Does the word "work" mean the same thing in "This dough does not work easily." and "He could not work the math problem."?

A: different meanings

Q: Does the word "connect" mean the same thing in "The new railroad will connect the northern part of the state to the southern part." and "My computer connected to his computer."?

A: the same meaning

Q: Does the word "drink" mean the same thing in "Can I buy you a drink?" and "He jumped into the drink and had to be rescued."?

A: different meanings

Q: Does the word "leak" mean the same thing in "He had to clean up the leak." and "A leak in a boat."?

A:
the same meaning