How to say "I will try to ..."?
みんなさん、初めまして！　日本語に質問があります。

Could anyone please be so kind as to tell me how would one say "I will try to..." in Japanese? Not in an "authentic" future fashion, such as "tomorrow I will try" or "in 3 years I will try", since I know there's no such thing in Japanese, but rather as in a pure expression of willingness to attempt something. For example:

- Today I will try to write in Japanese all day long.
- I'll try. (After being asked something)
- Please try to do it. (After asking somebody to do something)

Could anyone please translate these sentences for me?

ありがとうございます！

Question

How to say "I will try to ..."?
みんなさん、初めまして！　日本語に質問があります。

Could anyone please be so kind as to tell me how would one say "I will try to..." in Japanese? Not in an "authentic" future fashion, such as "tomorrow I will try" or "in 3 years I will try", since I know there's no such thing in Japanese, but rather as in a pure expression of willingness to attempt something. For example:

- Today I will try to write in Japanese all day long.
- I'll try. (After being asked something)
- Please try to do it. (After asking somebody to do something)

Could anyone please translate these sentences for me?

ありがとうございます！

Answer

- Today I will try to write in Japanese all day long.

今日は、一日中日本語で書いてみます。

- I'll try. (After being asked something)

やってみます。

- Please try to do it. (After asking somebody to do something)

やってみてください。

Answer

I think the most common way to say "I'll try to do sth" in Japanese is the structure "verbてform + みる"
The lady above mentioned つもり, but it's a marker of volition and feeling.
E.g.
今日は日本語で書いてみます。
I'll try to write in Japanese today.

Answer

I'll try : 試してやる
please try to do it: こんなおもちゃを試しなさい. 
Today I will try to write in Japanese all day long. : きょう日本語だけ書くつもりです or きょう日本語だけ書きためす。

I hope that I helped a little bit.