(Beraisa): Shimon ha'Pekuli arranged the 18 blessings of Shemoneh Esreh in front of R. Gamliel in Yavneh;
R. Gamliel: Does anyone know how to enact a blessing against heretics?
Shmuel ha'Katan enacted it; the next year, he [was leading the prayer and] forgot it; he spent two or three hours trying to remember it, they did not replace him.
Question: Why didn't they replace him?
(Rav Yehudah): If a Shali'ach Tzibur erred in any Berachah, we do not replace him, except for Birkas ha'Tzedukim, for we suspect he is a heretic (and therefore refuses to say it).
Answer: Since Shmuel ha'Katan himself enacted the blessing, we do not suspect him.
Question: Perhaps he retracted (and became a heretic)!
(Abaye): We have a tradition, a Tzadik will not become a Rasha.
Question: But it says, "uv'Shuv Tzadik mi'Tzidkaso v'Asah Avel..."!
Answer: That refers to one who originally was a Rasha, it would not happen to one who was a Tzadik from the beginning.
Question (Mishnah): Do not trust in yourself (that you will remain righteous) until you die!
Yochanan Kohen Gadol served for 80 years (even though almost every other Kohen Gadol in Bayis Sheni did not merit to live to serve a second year), and he became a Tzeduki in the end!
(Abaye): Yanai ha'Melech (who killed almost all the Chachamim) was Yochanan Kohen Gadol.
(Rava): They are different -- Yanai was a Rasha from the beginning, Yochanan was initially a Tzadik.
This is not difficult for Abaye (he can say that Yochanan was a Rasha from the beginning), but how can Rava answer?
Answer (for Rava): Even one who was initially a Tzadik can turn bad.
Question: If so, why didn't they replace Shimon ha'Tzadik?
Answer: He had started the blessing;
(Rav Yehudah): If a Shali'ach Tzibur does not begin Birkas ha'Tzedukim we replace him, but if he started it (and erred), we allow him to finish.
Question: To what do the seven blessings in the Shemoneh Esreh of Shabbos correspond?
Answer (R. Chalifta ben Shaul): They correspond to the seven "voices of Hash-m on the water" (mentioned in Tehilim 29).
Question: To what do the nine blessings in Musaf of Rosh Hashanah correspond?
Answer (R. Yitzchak of Kartignin): They correspond to the nine mentions of Hash-m's name in Chanah's prayer.
Pregnancy was decreed for Sarah, Rachel and Chanah on Rosh Hashanah. (From the text of the "u'Nesaneh Tokef" prayer, it seems that every pregnancy is decreed on Rosh Hashanah! Perhaps, since most people are Beinonim, the decree is not final until Yom Kipur, but for these righteous women, pregnancy was decreed and sealed on Rosh Hashanah.)
Question: On a public fast day [six blessings are added to the Shemoneh Esreh,] to what do the 24 blessings correspond?
Answer (R. Chelbo): They correspond to the 24 prayers that Shlomo said when he brought the Aron into the Kodesh ha'Kodashim.
Question: If so, we should say 24 blessings every day!
Answer: Shlomo said them on a day when mercy was needed (the gates did not want to let him enter), so we also say them on such days.
(Mishnah - R. Yehoshua): He may pray "like" Shemoneh Esreh.
Question: What is this?
Answer #1 (Rav): He says  abridged blessings;
Answer #2 (Shmuel): He says [the first three and last three blessings as usual; the middle blessings are condensed into one long one:] "Havinenu (endow us with wisdom)... to know Your ways... Baruch Atah Hash-m Shome'a Tefilah."
Abaye cursed one who would pray Havinenu (unless he was travelling).
(Rav Nachman): One may pray Havinenu any time of year, except for Motza'i Shabbos or Motza'i Yom Tov, for then one must say Havdalah in Chonen ha'Da'as (the fourth blessing, for understanding).
Question (Rabah bar Shmuel): He should be able to say Havdalah by itself as the fourth blessing!
(Mishnah - R. Akiva): [On Motza'i Shabbos or Motza'i Yom Tov] Havdalah is a blessing by itself, the fourth blessing.
R. Eliezer says, one says Havdalah in Modim.
Answer (Rav Nachman): The Halachah does not follow R. Akiva (regarding a standard Shemoneh Esreh), therefore it is unreasonable that for Havinenu we should follow his opinion;
The Halachah is unlike R. Akiva because the Anshei Keneses ha'Gedolah enacted 18 blessings, not 19 -- likewise, Havinenu was enacted with seven blessings, not eight!
Question (Mar Zutra): One should be able to make Havdalah part of the long middle blessing of Havinenu [and say], "Havinenu Hash-m Elokeinu ha'Mavdil Bein Kodesh l'Chol"!
This is left difficult.
(Rav Bivi bar Abaye): One may pray Havinenu any time of year, except for winter, for then one must request rain in Birkas ha'Shanim.
Question (Mar Zutra): One should be able to request rain in Havinenu [and say], "Prosper us in Your land, and give us rain..."!
Answer: A change from the standard text will confuse him (and make him forget the rest of the prayer).
Question: If so, one should not say Havdalah in Chonen ha'Da'as, lest this confuse him!
Answer: Havdalah is the beginning of the [requests of] Shemoneh Esreh, and thus it will not confuse him. We request rain in the middle of the requests, where a change will confuse him.
Question (Rav Ashi): One should be able to request rain in Shome'a Tefilah (it is the end of the requests, there is no concern for confusion)!
(R. Tanchum): If one forgot to mention rain in Techiyas ha'Mesim (the second blessing), he must go back; if one forgot to request rain in Birkas ha'Shanim, he need not go back, for he may request it in Shome'a Tefilah.
If one forgot to say Havdalah in Chonen ha'Da'as, he need not go back, for he can say it later over wine.
Answer: That is only for one who forgot; l'Chatchilah we do not request rain in Shome'a Tefilah.
(R. Tanchum): If one forgot... to request rain in Birkas ha'Shanim, he need not go back, for he may request it in Shome'a Tefilah.
Question (Beraisa): If one forgot to mention rain in Techiyas ha'Mesim or to request rain in Birkas ha'Shanim, he must go back;
If he forgot to say Havdalah in Chonen ha'Da'as, he need not go back, for he may say it later over wine.
Answer #1: One who prays with a Minyan need not go back, one who prays alone must go back.
Objection: Presumably, the distinction is that with a Minyan he need not go back because he will hear the request for rain from the Shali'ach Tzibur -- but R. Tanchum's reason was because he may request it in Shome'a Tefilah!
Answer #2: Rather, R. Tanchum also discusses one who prays alone;
If one remembers (that he forgot to request rain) before Shome'a Tefilah he need not repeat Shemoneh Esreh, for he may request it in Shome'a Tefilah; if he remembers after Shome'a Tefilah, he must repeat Shemoneh Esreh.
(R. Tanchum citing R. Yehoshua ben Levi): If one [realized that he] forgot to mention Rosh Chodesh (Ya'aleh v'Yavo) in Avodah (the blessing of Retzeh) and he is still in Avodah, he goes back to [the beginning of] Avodah;
If he remembered his omission while saying Modim or Sim Shalom, he goes back to Avodah; if he already finished his prayer, he repeats Shemoneh Esreh.
(Rav Papa brei d'Rav Acha): This law, that if he already finished his prayer he repeats Shemoneh Esreh, is only if he stepped back;
If not, he goes back to Avodah.
Question (R. Tanchum): What is your source for this?
Answer (Rav Papa): I heard this from my father, who heard it from Rav.
Version #1 (Rav Nachman bar Yitzchak): This law, that if he already stepped back, he repeats Shemoneh Esreh, is only if he does not normally add supplications after Shemoneh Esreh;
If he normally adds supplications after Shemoneh Esreh (it is as if he did not yet finish), he goes back to Avodah.
Version #2 (Rav Nachman bar Yitzchak): This law, that if he did not yet step back he goes back to Avodah, is only if he normally adds supplications after Shemoneh Esreh;
If not, he repeats Shemoneh Esreh.
THE PROPER WAY TO PRAY
(Mishnah - R. Eliezer): If one makes his prayer "fixed" ("Keva")...
Question: What does this mean?
Answer #1 (R. Yakov bar Idi): It is like a burden to him.
Answer #2 (Rabanan): He does not say it like supplications.
Answer #3 (Rabah and Rav Yosef): He is unable to [concentrate to] request something new.
R. Zeira: I could request something new, but I fear lest I would get confused (and be unable to resume Shemoneh Esreh).
Answer #4 (Abaye and R. Chanina bar Avin): This is one who does not pray (Shacharis and Minchah) Im Dimdumei Chamah (when the sun rises and sets).
(R. Chiya bar Aba): The Mitzvah (l'Chatchilah) is to pray Im Dimdumei Chamah.
(R. Zeira): He learns from "Yir'aucha Im Shamesh (Shacharis at sunrise) v'Lifnei Yare'ach Dor Dorim (Minchah before sunset)."
In Eretz Yisrael they would curse one who prayed Minchah before sunset.
Question: What is the reason?
Answer: It is possible that he will not pray in time.
(Mishnah - R. Yehoshua): One who travels in a dangerous place should say a short prayer: "[... May Yisrael's needs be in front of You] b'Chol Parashas ha'Ibur..."
Question: What does this mean?
Version #1 - Answer (Rav Chisda): It means, even when You are full of anger ("Avarah") at Yisrael, like a Me'uberes (a pregnant woman, whose womb is full).
Version #2 - Answer (Rav Chisda): It means, even when Yisrael transgress ("Ovrim") the Torah.
(Beraisa): One who travels in a place of wild animals and bandits prays a short prayer.
Question: What is this short prayer?
Answer #1 (R. Eliezer): "Do Your will in Heaven above and grant serenity to those who fear You below... Baruch Atah Hash-m Shome'a Tefilah."
Answer #2 (R. Yehoshua): "Hear the requests of Yisrael and speedily fulfill them; Baruch Atah Hash-m Shome'a Tefilah."
Answer #3 (R. Eliezer b'Rebbi Tzadok): "Hear the cries of Yisrael... Shome'a Tefilah."
Answer #4 (Acherim): "The needs of Yisrael are many, they do not know how to express them; may it be Your will to sustain every one and give him what he lacks; Baruch Atah Hash-m Shome'a Tefilah."
(Rav Huna): The Halachah follows Acherim.
Eliyahu (to Rav Yehudah, brother of Rav Sala Chasida): Do not get angry or drunk, lest you will sin;
Before travelling, consult with your Maker.
Question: What does this mean?
Answer (R. Yakov): You should say Tefilas ha'Derech (prayer for travelling).