I thought I had it but when we got to boxes, I got lost.
In Apple's new Dictionary app here's the following for both (I believe it's the Progressive Japanese-English dictionary):
ひらく【開く】
1 〔あける,あく〕open⇒あける(開ける)
ふたを開く|lift [take off] the lid
包みを開く|open [undo] a parcel / open [untie] a package
扇子を開く|open [unfold] a fan
本の38ページを開きなさい|Open your book(s) to [at] page 38.
戸はすぐに開いた|The door opened at once.
口を開く|open one's mouth (▼比喩的にも用いる)
彼が美術について最初に私の目を開いてくれた|He first opened my eyes to the arts.
開かれた大学にしなければならない|We must open up the university. / The university must not remain an ivory tower.
土地の人はよそ者になかなか心を開かない|The local people do not open up easily to strangers.
あける【開ける】
1 〔開く〕open; 〔包装などを〕undo
ドアを開ける|open a door / 〔鍵を使って〕unlock a door
ドアを乱暴に開ける|throw [fling] a door open
箱のふたを開ける|lift the lid of a box / open [take the lid off] a box
(本の) 25ページを開けなさい|[Open your book(s) at / Turn to] page 25.
窓を壊して開けた|He broke the window open.
窓は開けておいてください|Please leave the windows open.
包みを開ける|undo [unwrap] a package
夜中の12時まで鍵は開けておく|The door is left unlocked until twelve midnight.
Maybe Naomi先生 can do a lesson on this.