Your only pencil broke.
E.g. Can you lend me your pencil sharpener?
Your pencil fell down under your friend's chair.
E.g. Could you pick up my pencil?
You don't have a pencil.
E.g. Could you lend me a pencil?
The room is very cold.
E.g. Could you turn on the heater?
You meet your favorite idol.
e.g. Would you give me your signature?
Your friend has cookies and you're hungry.
E.g. Can I have a cookie?
You need your textbook in class but left it at home.
E.g. Can you share your textbook with me?
The class is very hot.
E.g. Would you turn on the air conditioner?
You need to use your friend's phone.
E.g. Would you lend me your phone?
You want your friend to sit with you.
E.g. Can you sit beside me?