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date                         約會

a meeting that you have arranged with a boyfriend or girlfriend or with somebody

who might become a boyfriend or girlfriend 

I've got a date with Lucy tomorrow night.                       

明天晚上我與露西有個約會。

http://www.google.com.tw/dictionary?langpair=en|zh-TW&q=date&hl=zh-TW&aq=f

appointment        約會

a formal arrangement to meet or visit somebody at a particular time,

especially for a reason connected with their work 

I've got a dental appointment at 3 o'clock. 

我約了下午 3 點看牙醫。

http://www.google.com.tw/dictionary?langpair=en|zh-TW&q=appointment&hl=zh-TW&aq=f